Okay. So Ive taken both of your ideas.
@Bob, with leads are you referring to the metal 'spokes' that the capacitors/resistors have on the underside of the PCB. If so, I will admit I have cut them as short as I can, but I am missing my proper Wire cutter so they are not properly cut, but none of them seem to be touching each other, and aside from that, Most if not all BOSS pedals are equipped with that plastic sheat you put on before the metal casing, so there is no way they can touch the case.
@Alan, once again I took your suggestion, I insulated the cables by the power input with masking tape (not sure if that does the job), however when I push down on the board it still messes up. And there are no cables trapped anywhere.
Just to give you guys more info, there were 3 cables that snapped off accidentally, 2 of them were from the Power input (blue and red one) and one gray one that was connected from the Input Jack Ground to the PCB. I connected all 3 of these tho. Another observation I made was when I push the bottom part of the PCB (The side away from the power) it freaks out my power more easier as in I need less force to push as opposed to higher up.
I'm not sure if this pic will help, But the area closest to where it has the BOSS logo seems to be the trouble area.