By shutoff do you mean games lock solid? Besides a possible bad dimm accounting for unexpected locks a board problem is likely since you ruled temps out. But can you monitor video card temps along with cpu and board?
A bad cap or biod eprom would be the hardware side of a board problem while a weak battery or corrupted bios programming would be another type. With XP games tend to lock up solid while Vista now sees an improved crash control method for logging off in order to return to the desktop if the task manager fails to end a locked game or app.
If you have a reset button that should readily see the system restart and bring up the Windows F8 boot menu for the last known that worked, safe mode, or starting Windows normally. The power button held should see the system turn off completely unless a board problem is present. You should see the "soft off in 4 seconds" or similar option in the bios setup along with the user defined option there in case that is set different.