i would start by removing the keys, and soak the board in 99% isopropyl, then scrub it with a new toothbrush. this will break away any corrosion, without causing the metals to oxidize. blow dry for a minute, then let sit for 30 minutes. see if that gts you key running. The fact that the switch is working, but the signal wont send means the damage to the trace could be nearly anywhere. finding it would be very difficult.