I think the problem is the oven expects specific wires to go to specific buttons. I think it will be better to try to trace as many wires as possible to get some idea how it worked. Try to post photos - someone may know it or have similar.
I just took a keyboard out of a boom box and the fifteen switches are wired as two voltage dividers. Just sayin'.
Contamination of the switch lubricant - or contact surfaces - over time causes spurious contact "closures" or mis-reads - "ciphers" and it becomes unserviceable.