well, I would try to reinstall the OS before making any radical moves. if that does not help next step would be to check ICs related to buttons. i dont know the internal structure of poly but i guess it consists of a main board (cpu, display etc) and a button/knobs board.
if that is the case try to disconnect the user interface board from the main board and see if the issue still persists. that should give some indication where the problem originates from in terms of topography.
edit: have checked 309. it uses HEF4051BT multiplexers and HC573 latches. your machine likely uses similar or same ICs. if the knobs/buttons board is causing the issue it could happen that one of those components is either faulty or joints would require a reflow.