Go into the BIOS and disable any Wake On LAN options. You will see a prompt
at the lower left-hand corner of your screen when you first turn on the
computer which will tell you what key to press to get into the BIOS.
I had one case where an optical trackball was turning a P/C on without help.
Either there was some vibration occurring at night, a cat was playing with
the trackball, or some other really odd cause existed.
Anyway, turning off the "wake" options for the trackball was the solution.