MacPro 5,1 won't start or wake up from sleep

Took it to Apple Store. It started every button press. Embarrassing.

Same issues after I got it home so I took it in.
They had problems this time, and said that it was related to loose RAM stick.
Strange. I don't move the machine, and it's worked fine for nearly 2 years.

Back home Deja Vu all over again. Video taped the problem and burned DVD on Mini. (38 button presses and 6 power cord removals before it started.)

Wrote up repair for new power supply and PC board that it is attached to. When I picked up the machine,they stated that the issue was a loose video card.(Really?) They ran the hardware test and didn't find any problems. No repair.

I discovered a low power reading from the UPS and plugged it in to another circuit (120 v).

Same issues. Sometimes it starts after 1 press ... or 3 ... or 8.
I'm glad that I have another year on Applecare.

Ideas on the cause? Will it help to speak with the manager?

I primarily use it for Logic, so I suppose that I could get by with one of the new Minis, but I need to get it working so that I can sell it.
Help!