Do you have (in Energy Saver) an automatic turn on at a specific time turned on? Restart after Power failure?
It could also be an issue of heat, so are your fans running? Or a power bar that went bad, strange but possible. I've had a computer at work do similar symptoms, and replacing the power bar was the strangest magic cure.
If not that, it could be a problem with the motherboard.
I still remember Macnutt.