Check Your network connection...

Open a terminal (ctrl-alt-T) and check if you are actually connected to the Internet with the following command:

ping 4.2.2.2

What kind of networking hardware? What's the output of

lspci

@starchild - a terminal show me a connection with net:
PING 4.2.2.2 (4.2.2.2) 56(84) bytes of data.
64 bytes from 4.2.2.2: icmp_req=1 ttl=47 time=70.7 ms
64 bytes from 4.2.2.2: icmp_req=2 ttl=47 time=68.9 ms
64 bytes from 4.2.2.2: icmp_req=3 ttl=47 time=71.5 ms
64 bytes from 4.2.2.2: icmp_req=4 ttl=47 time=65.3 ms
64 bytes from 4.2.2.2: icmp_req=5 ttl=47 time=66.2 ms
64 bytes from 4.2.2.2: icmp_req=6 ttl=47 time=66.9 ms
64 bytes from 4.2.2.2: icmp_req=7 ttl=47 time=73.8 ms
64 bytes from 4.2.2.2: icmp_req=8 ttl=47 time=67.9 ms
64 bytes from 4.2.2.2: icmp_req=9 ttl=47 time=66.9 ms
64 bytes from 4.2.2.2: icmp_req=11 ttl=47 time=61.1 ms
64 bytes from 4.2.2.2: icmp_req=12 ttl=47 time=67.2 ms
64 bytes from 4.2.2.2: icmp_req=13 ttl=47 time=64.6 ms
64 bytes from 4.2.2.2: icmp_req=14 ttl=47 time=64.0 ms
64 bytes from 4.2.2.2: icmp_req=15 ttl=47 time=61.9 ms
64 bytes from 4.2.2.2: icmp_req=16 ttl=47 time=65.3 ms
64 bytes from 4.2.2.2: icmp_req=17 ttl=47 time=63.6 ms
64 bytes from 4.2.2.2: icmp_req=18 ttl=47 time=64.3 ms
^C
--- 4.2.2.2 ping statistics ---
18 packets transmitted, 17 received, 5% packet loss, time 17029ms
rtt min/avg/max/mdev = 61.158/66.519/73.860/3.267 ms

@lembas I have a wi-fi Atheros card, and I send to us a answers from Abrowser from Trisquel GNU/Linux. A net works fine (without YouTube and Facebook) but I can't update a OS.

EDIT:

When I try to open a "Add/Remove Applications" this log was show to me:

GPG error: http://ftp.rediris.es brigantia InRelease: File /var/lib/apt/lists/partial/ftp.rediris.es_mirror_Trisquel_packages_dists_brigantia_InRelease doesn't start with a clearsigned messageGPG error: http://ftp.rediris.es brigantia-security InRelease: File /var/lib/apt/lists/partial/ftp.rediris.es_mirror_Trisquel_packages_dists_brigantia-security_InRelease doesn't start with a clearsigned messageGPG error: http://ftp.rediris.es brigantia-updates InRelease: File /var/lib/apt/lists/partial/ftp.rediris.es_mirror_Trisquel_packages_dists_brigantia-updates_InRelease doesn't start with a clearsigned messageNie udało się pobrać gzip:/var/lib/apt/lists/partial/ftp.rediris.es_mirror_Trisquel_packages_dists_brigantia_main_source_Sources Encountered a section with no Package: header
Nie udało się pobrać gzip:/var/lib/apt/lists/partial/ftp.rediris.es_mirror_Trisquel_packages_dists_brigantia_main_binary-i386_Packages Encountered a section with no Package: header
Nie udało się pobrać http://ftp.rediris.es/mirror/Trisquel/packages/dists/brigantia/main/i18n/Index Brak wpisu Hash w pliku Release /var/lib/apt/lists/partial/ftp.rediris.es_mirror_Trisquel_packages_dists_brigantia_main_i18n_Index
Nie udało się pobrać gzip:/var/lib/apt/lists/partial/ftp.rediris.es_mirror_Trisquel_packages_dists_brigantia-security_main_source_Sources Encountered a section with no Package: header
Nie udało się pobrać gzip:/var/lib/apt/lists/partial/ftp.rediris.es_mirror_Trisquel_packages_dists_brigantia-security_main_binary-i386_Packages Encountered a section with no Package: header
Nie udało się pobrać http://ftp.rediris.es/mirror/Trisquel/packages/dists/brigantia-security/main/i18n/Index Brak wpisu Hash w pliku Release /var/lib/apt/lists/partial/ftp.rediris.es_mirror_Trisquel_packages_dists_brigantia-security_main_i18n_Index
Nie udało się pobrać gzip:/var/lib/apt/lists/partial/ftp.rediris.es_mirror_Trisquel_packages_dists_brigantia-updates_main_source_Sources Encountered a section with no Package: header
Nie udało się pobrać gzip:/var/lib/apt/lists/partial/ftp.rediris.es_mirror_Trisquel_packages_dists_brigantia-updates_main_binary-i386_Packages Encountered a section with no Package: header
Nie udało się pobrać http://ftp.rediris.es/mirror/Trisquel/packages/dists/brigantia-updates/main/i18n/Index Brak wpisu Hash w pliku Release /var/lib/apt/lists/partial/ftp.rediris.es_mirror_Trisquel_packages_dists_brigantia-updates_main_i18n_Index
Some index files failed to download. They have been ignored, or old ones used instead.

You should change your repo address:

sudo nano /etc/apt/sources.list

and change "http://ftp.rediris.es/mirror/Trisquel/packages/" to "http://es.archive.trisquel.info/trisquel/"

save and exit.

sudo aptitude update

and you should be set.

Or with GUI: Update Manager > Settings > choose another mirror on "Download from" in "Trisquel Software" tab.

To explain a little further, ftp.redir.es was a repository mirror which came by default for Trisquel 5.5, and is now inactive (not working). To solve the problem do what starchild or icarolongo said.

Thanks icarolongo, I had the same problem and this worked. Unfortunately you still get directed to the defunct server when choosing to test for the best server automatically.