To help others see more of what's going on, I've supplied this link.
My parents have an eMachines desktop which was working fine until a couple weeks ago when Windows XP started shutting down almost as soon as they turned it on. Sometimes it completes the startup and is on for a few minutes before it shuts down. Other times it starts shutting down before the startup is complete.
What's really bizarre is that it also started powering up by itself after being turned off for several days. It wasn't just in hybernation mode, the switch had been turned off. They had to unplug it to get it to stop booting up in the middle of the night.