This is not good news. Considering what you have just described, it’s safe to say that you should abandon the console but salvage things like buttons, the new screen, and the digitiser. Apart from that, the fact that the volume up is mapped to d-pad down means there is some shorting or interferance taking place. The volume is controlled and passd through the daughter board on the (when opened) right side of the board.
If you have the patience of a saint, I would recommend going over each of the faulty connections with a multimeter and seeing what happens. Anything that looks dark or otherwise “different“, is a sign you’ll need to replace.
The fact you can diagnose this is a sign this may be salvagable; the console can turn on.