I am done re-wiring everything. Still no joy.
I am to the point where it's gotta be something on the board. If I go to the switch test page, everything works as it should except the joysticks. P4 joy controls are always on, as is the P4 start button. Obviously, if I unplug the P4 joy cable they go off. I can then unplug all the control cable harnesses until none are connected and P4 start is still on.
So, now what? Other than swapping out boards with someone who has a working or extra board, I'm out of ideas.
Pessimist: Oh, this can't get any worse!
Optimist: Yes, it can!