There is as good a chance as anything that you have a rootkit with a keylogger. Keyloggers, in a way that they access the keyboard controller chip, can trip the reset pin on the CPU which causes your computer to restart. The keyboard controller chip, that keyloggers manipulate, has a direct line to the reset pin on the CPU. Usually you can tell when your reset pin is being affected by noticing that your power switch on your PC will not work when you push it. Reset pins replaced manual power switches years ago, with the exception being the override switch on the power supply, which is located on the back of your PC towards the top.
If it is simply starting up on its own (not rebooting on its own) I would guess that unless you have a "boot from LAN" capability enabled, you are getting a power surge from a faulty power supply.