Coin counter will only work through the coin input and not the service switch. Think that board might have 2 coin inputs so you could try the other coin input as I think it has a separate circuit which probably controls other switches too. Coin inputs are just a switch input so with other switches not working it might suggest that you have a chip down, think midway used 7414s but there'll be other chips controlling it. Best to see if the other coin input works,have a look at the schematics and work out if your non-registering switches all are going to the same chip and hence the same input chain so to speak.
Good luck, I would think it's an easy non-expensive fix.