Hi Stolport,
Do you mean that the computer switches itself off and then restarts?
Or do you mean that when the computer is switched off it starts up all by its self?
If the first, in the absence of any other symptoms like lots of unexpected firewall traffic which could indicate a virus, I would check the processor cooling fan and the power supply fan. Most modern PC's automatically shut down if too hot.
If the PC is starting up by itself and you are using a network card to connect to a broadband router, as opposed to a USB modem, the network card / PC BIOS might have "Wake on LAN" enabled. This is a feature that lets administrators remotely switch on a PC to work on it. If this sounds possible just disable WoL and see if that does the trick.
My desktop PC has it enabled and although it is supposed to require a special set of packets to be sent to the card to start the PC, if connected to my router it sometimes just wakes up - i'm as sure as I can be that it is not a hack. I can't get it to work via my firewall and I know all the detalis, is seems just random. Made me jump the first time it happened though!
