PC crashes when running Dota2/Wow/Civ5/Portal2/Skyrim

Hi all, long time lurker first time poster

I'm having some problems with my computer at the moment.
When I try to run a game, it will play fine for 10 minutes or so then just turn itself off. At first I thought it was a PSU problem, so I went out and bought a brand new 500W PSU. Unfortuently, nothing has changed, and it keeps happening.

My specs are;

AMD Athlon 64 x2 dual core processor 6000+
4 gig RAM
500W power supply (new)
GTS Grfore 450 (link to gfx card, minimum power req. is 400W)

I should also note that I am running dual screens

Thanks guys, hopefully you can help me get on top of this

istandards