I would try cleaning the A/B/X/Y contacts with isopropyl alcohol.
I’m not sure where the screw would come from… I’m not as skilled in Xbox equipment.
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I don’t quite know about the bumpers either since those are soldered on buttons. my only idea is that the bottom board is bad. (the one without the sticks) But again, I’m not as skilled in Xbox equipment, so I don’t know if that is the problem.