idontlikeapple

It seems the video card is the problem ... ... it sounds like the video card shuts down itself after a while ... ... that can be due to overheat!? or ... ... the power supply does not have enough power!?  

Try to boot in BIOS and stay there for a while and see whether the monitor will turn black after 5 mins.

If you have ubuntu boot CD, then I will suggest to boot your computer using ubuntu boot CD and check the device etc.