Hi Michael...
I'm inclined to believe (as others have speculated) that your issue is motherboard related since you've diagnosed & verified the other potential problems.
Have you checked into the power button itself? Glennd mentioned several items to investigate, which included the physical switches, power switch,e tc.
Specifically 2 things. One, the plastic button itself. It should rebound once you have pressed the button to power on the unit. If it doesn't rebound, it could be the plastic hinge(?) (ie, the part of the button that lifts the button back into position).
Secondly, it could be the tiny switch on the motherboard. I've had a couple of these little switches go out over the years. Some are easy to fix (ie, has some sort of debris in the button), but others are sealed closed and would need a replacement.
Good luck with your repair.....
Cheers!