Is this a Vista PC or a XP PC? At 3AM is when most of the Windows Updates are automatically installed. So you would have to turn that feature off as that is what is most likely causeing the PC to turn on at that time.
Either that or turn off the monitor. If it is a laptop. Close the lid.
I do not accept support questions via EMail, PM, IM or my G+ page!
Phone: LG Optimus G Pro
Running: Stock JB from LG with Nova Launcher