I would repin J4 on the mpu, and reflow the solder on the header pins. Then move to the sound board and do the same. The fact that the sound board doesn't play the correct tunes indicates a problem either at the MPU where the signal leaves or the sound board where it comes in. Gotta address both connectors and headers to make sure.

bad connector between mpu j4 and driver j4.

female side of mpu j4 gets wasted by batteries. male side of driver j4 gets cracked solder joints from no plated through holes (most driver board versions).

To clarify, there are 2 types of solenoids on a Bally game. Momentary and continuous. From your description the continuous solenoids are working but the momentary are/were not.
The address lines for the momentary solenoids are shared by the sound board. There is a another line called the solenoid bank select. That line determines if the address is a sound or a momentary coil. If that line goes open or shorts you will only get sounds or coils. Sounds like that is your problem.
This is usually caused by a open solder connection or loose wire on it's pin. Follow Xenons advise above and make sure that wire is solid all the way through.