i have experience with this as i regualrly take mine apart for cleaning and i also mod and repair controllers.
the ps3 controllers are VERY temperamental during reassembly.. if you dont do it perfect you will end up making a problem worse. regular cleaning of the controller is a good idea. because that was likely the cause of your random button presses. its unlikely that dropping it caused the issue, so after you do a thorough cleaning TAKE YOUR TIME during the reassembly because thats probably where you went wrong.
the boards inside are pretty durable and broken ribbon inside would make the buttons not work AT ALL. your best bet is to try to take apart and reassemble it.
if that doesnt work, then its likely the board, in which case youre better off finding a new controller off ebay
hope i helped