First check the micro switch under the button by testing it for a closed circuit when the button is down. Next make sure the wires have not become disconnected or broken that lead from the pcb edge connector to the button. Last check the pcb edge connector to make sure no pins have come loose.
Nintendo makes really good quality parts. In my experience you can usually take the item apart and clean it and it will be fine. Otherwise, if you need some parts try Mike's arcade, etc.