Reboots on its own! That's handy, next there will be computers that type in programs and stuff on their own(broken keyboards do that, but not very well). ;-)
:-)
Sounds like a short, or an overheating problem.
Have you tried using it without the graphics card, since it sounds as though the display goes funny first, unplug that(after changing+saving the screenmode settings), and let it sit and run for a while.