Resolution stuck at 1400 x 1050 after updates

output of
lspci | grep VGA

(standard input):13:01:00.0 VGA compatible controller: Advanced Micro Devices, Inc. [AMD/ATI] Cedar [Radeon HD 5000/6000/7350/8350 Series]

You are one of the most unfortunate owners of an ATI GPU, which is an awful gpu for it requires nonfree firmware to work correctly. The libre kernel Jxself packages should at least give you the correct (native) resolution. Make sure you install and use (select in GRUB) the **latest** kernel (4.8) as on jxself's website.

https://jxself.org/linux-libre/

The real solution would be for you to sell your current laptop and buy one with an Intel gpu (just not the latest one, skyblob skylake). Without video acceleration those ATI gpus are useless crap :(

When I issue the following command
$ sudo apt-get install linux-libre64-lts
I get
Reading package lists... Done
Building dependency tree
Reading state information... Done
Some packages could not be installed. This may mean that you have
requested an impossible situation or if you are using the unstable
distribution that some required packages have not yet been created
or been moved out of Incoming.
The following information may help to resolve the situation:

The following packages have unmet dependencies:
linux-libre64-lts : Depends: linux-libre-lts but it is not installable
E: Unable to correct problems, you have held broken packages.
then $ sudo apt-get install linux-libre-lts
Reading package lists... Done
Building dependency tree
Reading state information... Done
Some packages could not be installed. This may mean that you have
requested an impossible situation or if you are using the unstable
distribution that some required packages have not yet been created
or been moved out of Incoming.
The following information may help to resolve the situation:

The following packages have unmet dependencies:
linux-libre-lts:i386 : Depends: freesh-keyring:i386 but it is not installable
E: Unable to correct problems, you have held broken packages.
and $ sudo apt-get install freesh-keyring
Reading package lists... Done
Building dependency tree
Reading state information... Done
freesh-keyring is already the newest version.
The following packages were automatically installed and are no longer required:
linux-headers-3.13.0-100 linux-headers-3.13.0-100-lowlatency
linux-headers-3.13.0-39 linux-headers-3.13.0-39-lowlatency
linux-headers-3.13.0-96 linux-headers-3.13.0-96-lowlatency
linux-image-3.13.0-100-lowlatency linux-image-3.13.0-39-lowlatency
linux-image-3.13.0-96-lowlatency
Use 'apt-get autoremove' to remove them.
0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded.
I then type $ sudo apt-get install linux-libre-4.1
Reading package lists... Done
Building dependency tree
Reading state information... Done
Some packages could not be installed. This may mean that you have
requested an impossible situation or if you are using the unstable
distribution that some required packages have not yet been created
or been moved out of Incoming.
The following information may help to resolve the situation:

The following packages have unmet dependencies:
linux-libre-4.1 : Depends: linux-image-4.135-gnu but it is not installable
Depends: linux-firmware-image-4.135-gnu but it is not installable
Depends: linux-headers-4.135-gnu but it is not installable
E: Unable to correct problems, you have held broken packages.
And before that when I tried to install linux-libre64-lts it just hang at the beggining. What to do? I did the update before this.

When I issue the following command
$ sudo apt-get install linux-libre64-lts
I get
Reading package lists... Done
Building dependency tree
Reading state information... Done
Some packages could not be installed. This may mean that you have
requested an impossible situation or if you are using the unstable
distribution that some required packages have not yet been created
or been moved out of Incoming.
The following information may help to resolve the situation:

The following packages have unmet dependencies:
linux-libre64-lts : Depends: linux-libre-lts but it is not installable
E: Unable to correct problems, you have held broken packages.
then $ sudo apt-get install linux-libre-lts
Reading package lists... Done
Building dependency tree
Reading state information... Done
Some packages could not be installed. This may mean that you have
requested an impossible situation or if you are using the unstable
distribution that some required packages have not yet been created
or been moved out of Incoming.
The following information may help to resolve the situation:

The following packages have unmet dependencies:
linux-libre-lts:i386 : Depends: freesh-keyring:i386 but it is not installable
E: Unable to correct problems, you have held broken packages.
and $ sudo apt-get install freesh-keyring
Reading package lists... Done
Building dependency tree
Reading state information... Done
freesh-keyring is already the newest version.
The following packages were automatically installed and are no longer required:
linux-headers-3.13.0-100 linux-headers-3.13.0-100-lowlatency
linux-headers-3.13.0-39 linux-headers-3.13.0-39-lowlatency
linux-headers-3.13.0-96 linux-headers-3.13.0-96-lowlatency
linux-image-3.13.0-100-lowlatency linux-image-3.13.0-39-lowlatency
linux-image-3.13.0-96-lowlatency
Use 'apt-get autoremove' to remove them.
0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded.
I then type $ sudo apt-get install linux-libre-4.1
Reading package lists... Done
Building dependency tree
Reading state information... Done
Some packages could not be installed. This may mean that you have
requested an impossible situation or if you are using the unstable
distribution that some required packages have not yet been created
or been moved out of Incoming.
The following information may help to resolve the situation:

The following packages have unmet dependencies:
linux-libre-4.1 : Depends: linux-image-4.135-gnu but it is not installable
Depends: linux-firmware-image-4.135-gnu but it is not installable
Depends: linux-headers-4.135-gnu but it is not installable
E: Unable to correct problems, you have held broken packages.
And before that when I tried to install linux-libre64-lts it just hang at the beggining. What to do? I did the update before this.

When I issue the following command
$ sudo apt-get install linux-libre64-lts
I get
Reading package lists... Done
Building dependency tree
Reading state information... Done
Some packages could not be installed. This may mean that you have
requested an impossible situation or if you are using the unstable
distribution that some required packages have not yet been created
or been moved out of Incoming.
The following information may help to resolve the situation:

The following packages have unmet dependencies:
linux-libre64-lts : Depends: linux-libre-lts but it is not installable
E: Unable to correct problems, you have held broken packages.
then $ sudo apt-get install linux-libre-lts
Reading package lists... Done
Building dependency tree
Reading state information... Done
Some packages could not be installed. This may mean that you have
requested an impossible situation or if you are using the unstable
distribution that some required packages have not yet been created
or been moved out of Incoming.
The following information may help to resolve the situation:

The following packages have unmet dependencies:
linux-libre-lts:i386 : Depends: freesh-keyring:i386 but it is not installable
E: Unable to correct problems, you have held broken packages.
and $ sudo apt-get install freesh-keyring
Reading package lists... Done
Building dependency tree
Reading state information... Done
freesh-keyring is already the newest version.
The following packages were automatically installed and are no longer required:
linux-headers-3.13.0-100 linux-headers-3.13.0-100-lowlatency
linux-headers-3.13.0-39 linux-headers-3.13.0-39-lowlatency
linux-headers-3.13.0-96 linux-headers-3.13.0-96-lowlatency
linux-image-3.13.0-100-lowlatency linux-image-3.13.0-39-lowlatency
linux-image-3.13.0-96-lowlatency
Use 'apt-get autoremove' to remove them.
0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded.
I then type $ sudo apt-get install linux-libre-4.1
Reading package lists... Done
Building dependency tree
Reading state information... Done
Some packages could not be installed. This may mean that you have
requested an impossible situation or if you are using the unstable
distribution that some required packages have not yet been created
or been moved out of Incoming.
The following information may help to resolve the situation:

The following packages have unmet dependencies:
linux-libre-4.1 : Depends: linux-image-4.135-gnu but it is not installable
Depends: linux-firmware-image-4.135-gnu but it is not installable
Depends: linux-headers-4.135-gnu but it is not installable
E: Unable to correct problems, you have held broken packages.
And before that when I tried to install linux-libre64-lts it just hang at the beggining. What to do? I did the update before this.

When I issue the following command
$ sudo apt-get install linux-libre64-lts
I get
Reading package lists... Done
Building dependency tree
Reading state information... Done
Some packages could not be installed. This may mean that you have
requested an impossible situation or if you are using the unstable
distribution that some required packages have not yet been created
or been moved out of Incoming.
The following information may help to resolve the situation:

The following packages have unmet dependencies:
linux-libre64-lts : Depends: linux-libre-lts but it is not installable
E: Unable to correct problems, you have held broken packages.
then $ sudo apt-get install linux-libre-lts
Reading package lists... Done
Building dependency tree
Reading state information... Done
Some packages could not be installed. This may mean that you have
requested an impossible situation or if you are using the unstable
distribution that some required packages have not yet been created
or been moved out of Incoming.
The following information may help to resolve the situation:

The following packages have unmet dependencies:
linux-libre-lts:i386 : Depends: freesh-keyring:i386 but it is not installable
E: Unable to correct problems, you have held broken packages.
and $ sudo apt-get install freesh-keyring
Reading package lists... Done
Building dependency tree
Reading state information... Done
freesh-keyring is already the newest version.
The following packages were automatically installed and are no longer required:
linux-headers-3.13.0-100 linux-headers-3.13.0-100-lowlatency
linux-headers-3.13.0-39 linux-headers-3.13.0-39-lowlatency
linux-headers-3.13.0-96 linux-headers-3.13.0-96-lowlatency
linux-image-3.13.0-100-lowlatency linux-image-3.13.0-39-lowlatency
linux-image-3.13.0-96-lowlatency
Use 'apt-get autoremove' to remove them.
0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded.
I then type $ sudo apt-get install linux-libre-4.1
Reading package lists... Done
Building dependency tree
Reading state information... Done
Some packages could not be installed. This may mean that you have
requested an impossible situation or if you are using the unstable
distribution that some required packages have not yet been created
or been moved out of Incoming.
The following information may help to resolve the situation:

The following packages have unmet dependencies:
linux-libre-4.1 : Depends: linux-image-4.135-gnu but it is not installable
Depends: linux-firmware-image-4.135-gnu but it is not installable
Depends: linux-headers-4.135-gnu but it is not installable
E: Unable to correct problems, you have held broken packages.
And before that when I tried to install linux-libre64-lts it just hang at the beggining. What to do? I did the update before this.

When I issue the following command
$ sudo apt-get install linux-libre64-lts
I get
Reading package lists... Done
Building dependency tree
Reading state information... Done
Some packages could not be installed. This may mean that you have
requested an impossible situation or if you are using the unstable
distribution that some required packages have not yet been created
or been moved out of Incoming.
The following information may help to resolve the situation:

The following packages have unmet dependencies:
linux-libre64-lts : Depends: linux-libre-lts but it is not installable
E: Unable to correct problems, you have held broken packages.
then $ sudo apt-get install linux-libre-lts
Reading package lists... Done
Building dependency tree
Reading state information... Done
Some packages could not be installed. This may mean that you have
requested an impossible situation or if you are using the unstable
distribution that some required packages have not yet been created
or been moved out of Incoming.
The following information may help to resolve the situation:

The following packages have unmet dependencies:
linux-libre-lts:i386 : Depends: freesh-keyring:i386 but it is not installable
E: Unable to correct problems, you have held broken packages.
and $ sudo apt-get install freesh-keyring
Reading package lists... Done
Building dependency tree
Reading state information... Done
freesh-keyring is already the newest version.
The following packages were automatically installed and are no longer required:
linux-headers-3.13.0-100 linux-headers-3.13.0-100-lowlatency
linux-headers-3.13.0-39 linux-headers-3.13.0-39-lowlatency
linux-headers-3.13.0-96 linux-headers-3.13.0-96-lowlatency
linux-image-3.13.0-100-lowlatency linux-image-3.13.0-39-lowlatency
linux-image-3.13.0-96-lowlatency
Use 'apt-get autoremove' to remove them.
0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded.
I then type $ sudo apt-get install linux-libre-4.1
Reading package lists... Done
Building dependency tree
Reading state information... Done
Some packages could not be installed. This may mean that you have
requested an impossible situation or if you are using the unstable
distribution that some required packages have not yet been created
or been moved out of Incoming.
The following information may help to resolve the situation:

The following packages have unmet dependencies:
linux-libre-4.1 : Depends: linux-image-4.135-gnu but it is not installable
Depends: linux-firmware-image-4.135-gnu but it is not installable
Depends: linux-headers-4.135-gnu but it is not installable
E: Unable to correct problems, you have held broken packages.
And before that when I tried to install linux-libre64-lts it just hang at the beggining. What to do? I did the update before this.

When I issue the following command
$ sudo apt-get install linux-libre64-lts
I get
Reading package lists... Done
Building dependency tree
Reading state information... Done
Some packages could not be installed. This may mean that you have
requested an impossible situation or if you are using the unstable
distribution that some required packages have not yet been created
or been moved out of Incoming.
The following information may help to resolve the situation:

The following packages have unmet dependencies:
linux-libre64-lts : Depends: linux-libre-lts but it is not installable
E: Unable to correct problems, you have held broken packages.
then $ sudo apt-get install linux-libre-lts
Reading package lists... Done
Building dependency tree
Reading state information... Done
Some packages could not be installed. This may mean that you have
requested an impossible situation or if you are using the unstable
distribution that some required packages have not yet been created
or been moved out of Incoming.
The following information may help to resolve the situation:

The following packages have unmet dependencies:
linux-libre-lts:i386 : Depends: freesh-keyring:i386 but it is not installable
E: Unable to correct problems, you have held broken packages.
and $ sudo apt-get install freesh-keyring
Reading package lists... Done
Building dependency tree
Reading state information... Done
freesh-keyring is already the newest version.
The following packages were automatically installed and are no longer required:
linux-headers-3.13.0-100 linux-headers-3.13.0-100-lowlatency
linux-headers-3.13.0-39 linux-headers-3.13.0-39-lowlatency
linux-headers-3.13.0-96 linux-headers-3.13.0-96-lowlatency
linux-image-3.13.0-100-lowlatency linux-image-3.13.0-39-lowlatency
linux-image-3.13.0-96-lowlatency
Use 'apt-get autoremove' to remove them.
0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded.
I then type $ sudo apt-get install linux-libre-4.1
Reading package lists... Done
Building dependency tree
Reading state information... Done
Some packages could not be installed. This may mean that you have
requested an impossible situation or if you are using the unstable
distribution that some required packages have not yet been created
or been moved out of Incoming.
The following information may help to resolve the situation:

The following packages have unmet dependencies:
linux-libre-4.1 : Depends: linux-image-4.135-gnu but it is not installable
Depends: linux-firmware-image-4.135-gnu but it is not installable
Depends: linux-headers-4.135-gnu but it is not installable
E: Unable to correct problems, you have held broken packages.
And before that when I tried to install linux-libre64-lts it just hang at the beggining. What to do? I did the update before this.

When I issue the following command
$ sudo apt-get install linux-libre64-lts
I get
Reading package lists... Done
Building dependency tree
Reading state information... Done
Some packages could not be installed. This may mean that you have
requested an impossible situation or if you are using the unstable
distribution that some required packages have not yet been created
or been moved out of Incoming.
The following information may help to resolve the situation:

The following packages have unmet dependencies:
linux-libre64-lts : Depends: linux-libre-lts but it is not installable
E: Unable to correct problems, you have held broken packages.
then $ sudo apt-get install linux-libre-lts
Reading package lists... Done
Building dependency tree
Reading state information... Done
Some packages could not be installed. This may mean that you have
requested an impossible situation or if you are using the unstable
distribution that some required packages have not yet been created
or been moved out of Incoming.
The following information may help to resolve the situation:

The following packages have unmet dependencies:
linux-libre-lts:i386 : Depends: freesh-keyring:i386 but it is not installable
E: Unable to correct problems, you have held broken packages.
and $ sudo apt-get install freesh-keyring
Reading package lists... Done
Building dependency tree
Reading state information... Done
freesh-keyring is already the newest version.
The following packages were automatically installed and are no longer required:
linux-headers-3.13.0-100 linux-headers-3.13.0-100-lowlatency
linux-headers-3.13.0-39 linux-headers-3.13.0-39-lowlatency
linux-headers-3.13.0-96 linux-headers-3.13.0-96-lowlatency
linux-image-3.13.0-100-lowlatency linux-image-3.13.0-39-lowlatency
linux-image-3.13.0-96-lowlatency
Use 'apt-get autoremove' to remove them.
0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded.
I then type $ sudo apt-get install linux-libre-4.1
Reading package lists... Done
Building dependency tree
Reading state information... Done
Some packages could not be installed. This may mean that you have
requested an impossible situation or if you are using the unstable
distribution that some required packages have not yet been created
or been moved out of Incoming.
The following information may help to resolve the situation:

The following packages have unmet dependencies:
linux-libre-4.1 : Depends: linux-image-4.135-gnu but it is not installable
Depends: linux-firmware-image-4.135-gnu but it is not installable
Depends: linux-headers-4.135-gnu but it is not installable
E: Unable to correct problems, you have held broken packages.
And before that when I tried to install linux-libre64-lts it just hang at the beggining. What to do? I did the update before this.

When I issue the following command
$ sudo apt-get install linux-libre64-lts
I get
Reading package lists... Done
Building dependency tree
Reading state information... Done
Some packages could not be installed. This may mean that you have
requested an impossible situation or if you are using the unstable
distribution that some required packages have not yet been created
or been moved out of Incoming.
The following information may help to resolve the situation:

The following packages have unmet dependencies:
linux-libre64-lts : Depends: linux-libre-lts but it is not installable
E: Unable to correct problems, you have held broken packages.
then $ sudo apt-get install linux-libre-lts
Reading package lists... Done
Building dependency tree
Reading state information... Done
Some packages could not be installed. This may mean that you have
requested an impossible situation or if you are using the unstable
distribution that some required packages have not yet been created
or been moved out of Incoming.
The following information may help to resolve the situation:

The following packages have unmet dependencies:
linux-libre-lts:i386 : Depends: freesh-keyring:i386 but it is not installable
E: Unable to correct problems, you have held broken packages.
and $ sudo apt-get install freesh-keyring
Reading package lists... Done
Building dependency tree
Reading state information... Done
freesh-keyring is already the newest version.
The following packages were automatically installed and are no longer required:
linux-headers-3.13.0-100 linux-headers-3.13.0-100-lowlatency
linux-headers-3.13.0-39 linux-headers-3.13.0-39-lowlatency
linux-headers-3.13.0-96 linux-headers-3.13.0-96-lowlatency
linux-image-3.13.0-100-lowlatency linux-image-3.13.0-39-lowlatency
linux-image-3.13.0-96-lowlatency
Use 'apt-get autoremove' to remove them.
0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded.
I then type $ sudo apt-get install linux-libre-4.1
Reading package lists... Done
Building dependency tree
Reading state information... Done
Some packages could not be installed. This may mean that you have
requested an impossible situation or if you are using the unstable
distribution that some required packages have not yet been created
or been moved out of Incoming.
The following information may help to resolve the situation:

The following packages have unmet dependencies:
linux-libre-4.1 : Depends: linux-image-4.135-gnu but it is not installable
Depends: linux-firmware-image-4.135-gnu but it is not installable
Depends: linux-headers-4.135-gnu but it is not installable
E: Unable to correct problems, you have held broken packages.
And before that when I tried to install linux-libre64-lts it just hang at the beggining. What to do? I did the update before this.

When I issue the following command
$ sudo apt-get install linux-libre64-lts
I get
Reading package lists... Done
Building dependency tree
Reading state information... Done
Some packages could not be installed. This may mean that you have
requested an impossible situation or if you are using the unstable
distribution that some required packages have not yet been created
or been moved out of Incoming.
The following information may help to resolve the situation:

The following packages have unmet dependencies:
linux-libre64-lts : Depends: linux-libre-lts but it is not installable
E: Unable to correct problems, you have held broken packages.
then $ sudo apt-get install linux-libre-lts
Reading package lists... Done
Building dependency tree
Reading state information... Done
Some packages could not be installed. This may mean that you have
requested an impossible situation or if you are using the unstable
distribution that some required packages have not yet been created
or been moved out of Incoming.
The following information may help to resolve the situation:

The following packages have unmet dependencies:
linux-libre-lts:i386 : Depends: freesh-keyring:i386 but it is not installable
E: Unable to correct problems, you have held broken packages.
and $ sudo apt-get install freesh-keyring
Reading package lists... Done
Building dependency tree
Reading state information... Done
freesh-keyring is already the newest version.
The following packages were automatically installed and are no longer required:
linux-headers-3.13.0-100 linux-headers-3.13.0-100-lowlatency
linux-headers-3.13.0-39 linux-headers-3.13.0-39-lowlatency
linux-headers-3.13.0-96 linux-headers-3.13.0-96-lowlatency
linux-image-3.13.0-100-lowlatency linux-image-3.13.0-39-lowlatency
linux-image-3.13.0-96-lowlatency
Use 'apt-get autoremove' to remove them.
0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded.
I then type $ sudo apt-get install linux-libre-4.1
Reading package lists... Done
Building dependency tree
Reading state information... Done
Some packages could not be installed. This may mean that you have
requested an impossible situation or if you are using the unstable
distribution that some required packages have not yet been created
or been moved out of Incoming.
The following information may help to resolve the situation:

The following packages have unmet dependencies:
linux-libre-4.1 : Depends: linux-image-4.135-gnu but it is not installable
Depends: linux-firmware-image-4.135-gnu but it is not installable
Depends: linux-headers-4.135-gnu but it is not installable
E: Unable to correct problems, you have held broken packages.
And before that when I tried to install linux-libre64-lts it just hang at the beggining. What to do? I did the update before this.

When I issue the following command
$ sudo apt-get install linux-libre64-lts
I get
Reading package lists... Done
Building dependency tree
Reading state information... Done
Some packages could not be installed. This may mean that you have
requested an impossible situation or if you are using the unstable
distribution that some required packages have not yet been created
or been moved out of Incoming.
The following information may help to resolve the situation:

The following packages have unmet dependencies:
linux-libre64-lts : Depends: linux-libre-lts but it is not installable
E: Unable to correct problems, you have held broken packages.
then $ sudo apt-get install linux-libre-lts
Reading package lists... Done
Building dependency tree
Reading state information... Done
Some packages could not be installed. This may mean that you have
requested an impossible situation or if you are using the unstable
distribution that some required packages have not yet been created
or been moved out of Incoming.
The following information may help to resolve the situation:

The following packages have unmet dependencies:
linux-libre-lts:i386 : Depends: freesh-keyring:i386 but it is not installable
E: Unable to correct problems, you have held broken packages.
and $ sudo apt-get install freesh-keyring
Reading package lists... Done
Building dependency tree
Reading state information... Done
freesh-keyring is already the newest version.
The following packages were automatically installed and are no longer required:
linux-headers-3.13.0-100 linux-headers-3.13.0-100-lowlatency
linux-headers-3.13.0-39 linux-headers-3.13.0-39-lowlatency
linux-headers-3.13.0-96 linux-headers-3.13.0-96-lowlatency
linux-image-3.13.0-100-lowlatency linux-image-3.13.0-39-lowlatency
linux-image-3.13.0-96-lowlatency
Use 'apt-get autoremove' to remove them.
0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded.
I then type $ sudo apt-get install linux-libre-4.1
Reading package lists... Done
Building dependency tree
Reading state information... Done
Some packages could not be installed. This may mean that you have
requested an impossible situation or if you are using the unstable
distribution that some required packages have not yet been created
or been moved out of Incoming.
The following information may help to resolve the situation:

The following packages have unmet dependencies:
linux-libre-4.1 : Depends: linux-image-4.135-gnu but it is not installable
Depends: linux-firmware-image-4.135-gnu but it is not installable
Depends: linux-headers-4.135-gnu but it is not installable
E: Unable to correct problems, you have held broken packages.
And before that when I tried to install linux-libre64-lts it just hang at the beggining. What to do? I did the update before this.

When I issue the following command
$ sudo apt-get install linux-libre64-lts
I get
Reading package lists... Done
Building dependency tree
Reading state information... Done
Some packages could not be installed. This may mean that you have
requested an impossible situation or if you are using the unstable
distribution that some required packages have not yet been created
or been moved out of Incoming.
The following information may help to resolve the situation:

The following packages have unmet dependencies:
linux-libre64-lts : Depends: linux-libre-lts but it is not installable
E: Unable to correct problems, you have held broken packages.
then $ sudo apt-get install linux-libre-lts
Reading package lists... Done
Building dependency tree
Reading state information... Done
Some packages could not be installed. This may mean that you have
requested an impossible situation or if you are using the unstable
distribution that some required packages have not yet been created
or been moved out of Incoming.
The following information may help to resolve the situation:

The following packages have unmet dependencies:
linux-libre-lts:i386 : Depends: freesh-keyring:i386 but it is not installable
E: Unable to correct problems, you have held broken packages.
and $ sudo apt-get install freesh-keyring
Reading package lists... Done
Building dependency tree
Reading state information... Done
freesh-keyring is already the newest version.
The following packages were automatically installed and are no longer required:
linux-headers-3.13.0-100 linux-headers-3.13.0-100-lowlatency
linux-headers-3.13.0-39 linux-headers-3.13.0-39-lowlatency
linux-headers-3.13.0-96 linux-headers-3.13.0-96-lowlatency
linux-image-3.13.0-100-lowlatency linux-image-3.13.0-39-lowlatency
linux-image-3.13.0-96-lowlatency
Use 'apt-get autoremove' to remove them.
0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded.
I then type $ sudo apt-get install linux-libre-4.1
Reading package lists... Done
Building dependency tree
Reading state information... Done
Some packages could not be installed. This may mean that you have
requested an impossible situation or if you are using the unstable
distribution that some required packages have not yet been created
or been moved out of Incoming.
The following information may help to resolve the situation:

The following packages have unmet dependencies:
linux-libre-4.1 : Depends: linux-image-4.135-gnu but it is not installable
Depends: linux-firmware-image-4.135-gnu but it is not installable
Depends: linux-headers-4.135-gnu but it is not installable
E: Unable to correct problems, you have held broken packages.
And before that when I tried to install linux-libre64-lts it just hang at the beggining. What to do? I did the update before this.

When I issue the following command
$ sudo apt-get install linux-libre64-lts
I get
Reading package lists... Done
Building dependency tree
Reading state information... Done
Some packages could not be installed. This may mean that you have
requested an impossible situation or if you are using the unstable
distribution that some required packages have not yet been created
or been moved out of Incoming.
The following information may help to resolve the situation:

The following packages have unmet dependencies:
linux-libre64-lts : Depends: linux-libre-lts but it is not installable
E: Unable to correct problems, you have held broken packages.
then $ sudo apt-get install linux-libre-lts
Reading package lists... Done
Building dependency tree
Reading state information... Done
Some packages could not be installed. This may mean that you have
requested an impossible situation or if you are using the unstable
distribution that some required packages have not yet been created
or been moved out of Incoming.
The following information may help to resolve the situation:

The following packages have unmet dependencies:
linux-libre-lts:i386 : Depends: freesh-keyring:i386 but it is not installable
E: Unable to correct problems, you have held broken packages.
and $ sudo apt-get install freesh-keyring
Reading package lists... Done
Building dependency tree
Reading state information... Done
freesh-keyring is already the newest version.
The following packages were automatically installed and are no longer required:
linux-headers-3.13.0-100 linux-headers-3.13.0-100-lowlatency
linux-headers-3.13.0-39 linux-headers-3.13.0-39-lowlatency
linux-headers-3.13.0-96 linux-headers-3.13.0-96-lowlatency
linux-image-3.13.0-100-lowlatency linux-image-3.13.0-39-lowlatency
linux-image-3.13.0-96-lowlatency
Use 'apt-get autoremove' to remove them.
0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded.
I then type $ sudo apt-get install linux-libre-4.1
Reading package lists... Done
Building dependency tree
Reading state information... Done
Some packages could not be installed. This may mean that you have
requested an impossible situation or if you are using the unstable
distribution that some required packages have not yet been created
or been moved out of Incoming.
The following information may help to resolve the situation:

The following packages have unmet dependencies:
linux-libre-4.1 : Depends: linux-image-4.135-gnu but it is not installable
Depends: linux-firmware-image-4.135-gnu but it is not installable
Depends: linux-headers-4.135-gnu but it is not installable
E: Unable to correct problems, you have held broken packages.
And before that when I tried to install linux-libre64-lts it just hang at the beggining. What to do? I did the update before this.

Yes, I know it is overkill, but that seemed to be, upon a quick read I gave it, quite a serious hell.

>I don't know why you're trying to install linux-libre64-lts. This is one of the old meta packages and the current website makes no mention of them.

Yeah, I noticed that too. Hence I wrote to "follow carefully" the instructions on your site.

OP, first try to fix, if you see you spent a lot of time without having managed to fix it, then maybe reinstalling is a good option. But, yeah, try first to fix the dependency issue. Use synaptic for convenience and ease.
cheers

I tried to install linux-libre64-4.1, but it requested linux-libre-4.1 it said it's not going to be installed when I try it's stuck at 0%.

I tried again a couple times but I still can't install it using this command sudo apt install linux-libre-4.1. The command is from the guide, I did everything again from begging to end according to the guide, but it's just stuck to 0%

I don't really understand what I am supposed to do now with checking the connection. It's obviously alright since i can install any package except this kernel update. I proved that I can install any package. So the problem must be with this particular package. I don't know what it could be.

My sources.list:
# deb cdrom:[Trisquel 7.0 _belenos_ - Release amd64 (20141102)]/ belenos main

# Trisquel repositories for supported software and updates
deb http://es.archive.trisquel.info/trisquel/ belenos main
deb-src http://es.archive.trisquel.info/trisquel/ belenos main
deb http://es.archive.trisquel.info/trisquel/ belenos-security main
deb-src http://es.archive.trisquel.info/trisquel/ belenos-security main
deb http://es.archive.trisquel.info/trisquel/ belenos-updates main
deb-src http://es.archive.trisquel.info/trisquel/ belenos-updates main
# deb http://es.archive.trisquel.info/trisquel/ belenos-backports main
# deb-src http://es.archive.trisquel.info/trisquel/ belenos-backports main
deb https://linux-libre.fsfla.org/pub/linux-libre/freesh/ freesh main
I don't really understand the output of traceroute linux-libre.fsfla.org Should I post that too?

Could it have anything to do with the "https" protocol (e.g. unrecognized CA)?

EDIT: Just checked plain http and it works. So I would suggest retrying with http instead.

So I installed it succesfuly thanks to your help, but the resolution is still stuck at 1400x1050. Thanks to Abdullah Ramazanoglu's suggestion, I saw that the error was in https so I changed it to http. Thanks again!