BSOD 1-3 Times a Day, Usually While Not In Use

Hello, I could use some help figuring out why my system is throwing almost daily BSODs. First, a bit of background (maybe excessive, but could be helpful). I have a Dell XPS 720. My boyfriend bought it in March 2008 and ran it with Windows XP and loved it. Earlier this year, he upgraded it to Windows 7 Ultimate so he could expand the RAM and began experiencing numerous BSODs and...