When you said the connectors look OK did you pull the boards off and look at the header pin solder joints for cracking? Almost every old game has cracked joints. Fix those first. And double check continuity between the wiring for the speaker and volume pot to eliminate them
Next take a look at the sockets for the proms, if they are scanbe sockets they need replaced. And if the legs are black or tarnished the proms will need replaced as well.
The sound board gets AC power in the upper right connector, goes through the 2 fuses, through the bridge rectifier to make +12v and -12v, and then +12v is regulated by a 7805 to make the +5v. Check all of those to make sure you have the correct power available on the board.
After that there is a whole bunch more to investigate, but I'll let the pros take over. Pinwiki has a bunch of information about the type 1 and 2 sound boards.