Hmm, mine has a different problem that's a bit similar...
My computer randomly likes to put itself onto sleep mode during the night, even when the settings are set not to. It sometimes goes to sleep mode, but sometimes doesn't, which is bad because I need to charge my iPod Touch, and when my computers on sleep mode, it doesn't charge my iPod for some reason. It keeps charging my phone, though.
I still have not been able to fix this...
Anyway, to your problem, it may be because of something in your BIOS set to turn it on. If you can't find anything in the BIOS, take out the BIOS battery, remove all power from the computer, push the power button several times to drain all the power out, put the BIOS battery back in, and plug in your computer again.