Wiping Windows 7 hard drive without Windows password

I have been aware of other options other than Windows and Mac since I was around 8. However, I lived in my parent's home in a city which offered no internet access other than on Windows and Mac---although apparently my parents wouldn't have minded the idea of free software, since I was using Win98 til 2009 at home.

Eventually I moved and I have two laptops, both Windows, one is bad and the other is totally broken---in that I don't have the Windows password because I had to reset everything and change the password and something went wrong.

Can I use DBAS on a computer with only Win7 to wipe the hard drive without actually logging in to Windows, and how? Then, is Trisquel possible to install on a blank hard drive?

Here are the specs, roughly:

http://h10025.www1.hp.com/ewfrf/wc/document?cc=us&lc=en&dlc=en&docname=c02974952

To be clear, I don't need much and that is part of my motivation. My only slight irritation will be that LibreOffice's docx support isn't perfect and I am a college student in a Windows world, but I can work around that.

Also I need really, really fast internet, and in my current city that is pretty much only Time Warner. I need to know what needs to be installed to make that work.