When it turns off does the motherboard go out (as in, Windows halts, no sound plays, etc)? Even if the motherboard is indeed fried and halted, the drives are still getting power and will still spin. Check to make sure your motherboard isn't overheating, also check your graphics card to make sure it isn't overheating. It sounds like a motherboard problem to me, because mouse and keyboard are directly handled by the motherboard, as is basic video (while more advanced video is handled on the graphics card, but that receives its signal from the motherboard, and that allows for a motherboard problem).
Keep an eye on the temperatures. I use PC Wizard 2008 to monitor my PC (CPUID
) temperatures. Try running some sort of stress test (something that runs your CPU at 100% for a long period of time) to see if that causes it to stop running faster.