Shoot, shoulda thought of this last night, but I think you've exhausted the complex, it's starting to sound mechanical to me, dude you could have a bad power switch, no kidding I have seen this behavior a lot of times. Check your power switch, take the switch itself out and check the connections, look for burns or broken traces. Sometimes the little plastic switch itself can hang juuuuuuuuust slightly on it's housing. Check your keyboard for the same issue, any sticking or partially sticking keys can throw a monkey wrench into the works. Unplug peripherals like the front USB connections and see if it goes away, saw a tiny circuit board burn slightly one time and it stopped the whole system from booting.
That spontaneously turning-on thing you just mentioned is a big red flag pointing to a mechanical problem IMO.