Check continuity from the connector headers to the next step in the circuit, you'll probably want to look at the schematics but you can also just trace the traces. On my Bride of Pinbot (early WPC), some of the switch traces were intermittent between the headers and the board... I ended up replacing the headers (and the connector from the cabinet, because they were poorly hacked), and I still had to make a jumper to fix a broken trace :/
It looks like the start button is in the switch matrix (column 1, row 3), so I would expect to see similar problems in the same row or column, and I think there are enough useful switches on column 1 and switches on row 3 that you would notice something else.
Another thing to check with the continuity meter:
CPU board J206 and J207 should be the same circuit wise, so verify pin 1 to pin 1, etc. The manual says the connector from the playfield will be on J207, and J206 will be not connected, but you can swap them.
Same for J208 and J209 (manual says use J209, but J208 _might_ work better if something is damaged).
All of these are below the battery holder, so if there is a problem you can find, you might want to check for acid damage.
Hope this helps (even if it wasn't timely)