Why no power after pushing power button on front?

Yesterday my Mac Pro 1,1 shutdown all by itself (I was out of the room). It is connected to a battery backup. Today it would not start. No lights. No sound. Nothing. Plugged it into another confirmed power outlet. Still nothing. Even held power button down for :15-:20. I am replacing the internal memory battery CR 2032. How would I trouble shoot the power supply?

I am having a re-built power supply installed.