PC starts itself

Here is a very nysterious problem. I have a client who has a computer running Windows 2000 Pro with SP3. This PC is not very old at all, perhaps 2 years at the most. It runs very well without any conflicts at all, has plenty of ram, free hard drive space etc.
The problem:
After proper shut down of the computer, it will restart itself 30 to 60 minutes later with no user interaction at all.

Any suggestions?