Computer Turns Itself On

For about a week, my computer has been turning itself on at odd times (no conistentcy of times, but mostly in the middle of the night). It seems to work fine, but once I shut it down, it then does not want to boot up again. I usually have to unplugall from the computer and power source as well as toggle the powerbutton in the back of the computer. Nothing consistent to get it on, it just turns on eventually. Any ideas as to what is happening? Thanks