Power Supply Problem?

Hello all,

Trying to play Skyrim on an aging Core2Duo computer with a 7950gt. Wasn't having a great gameplay experience so a friend of mine let me borrow his GTX260. I start up the game and after about 30 seconds my computer crashes.

CPU: Core2Duo 2.4ghz
MB: ASUS P5B Deluxe
HDD: WD Black 500gb
GPU: GTX 260

PSU: Kingwinn ABT-600MA1 600 watt with 2 20A Rails. 5+ years old.

Computer seems to run ok at idle with no crashes. Only when I start up Skyrim.
Will it hurt the GPU to keep using it for non gaming tasks?

Thanks
Jon