They are not really worth the time for me to fix the originals anymore now that I am selling repros.
Since you get some sound out i'd assume the CPU is running at least somewhat and the amplifier stuff is OK
What does the button on the -51 sound board do? Does it play a noise? You can push the sound board NMI button and then watch the connections between the PIA and Sound generator for activity. The chirper in my logic probe will play the sound fairly clearly on some of the sound generator pins. I always do that to see if the sound board computer is running OK.
Next up I would look at the input signals....
The MPU sends four or five signals to the sound board. These inputs are buffered and inverted by the 4049 chip. Make sure all of them work (use sound test). Watch with probe input connector, through the 4049, and to the sound generator.
If you have digital sounding faults when pushing the NMI button, swap the ram, pia, rom, sound gen one at time with known good to see if there is a change.
These boards are pretty straight forward. Assuming the connectors and caps are ok. The magic is all done by the four big chips, not a lot else to go wrong. If the 4011 was bad no sound (no reset, no rom cs). If the sound is really soft and can't be adjusted, lm3900. No sound but computer is working, introduce hum into the main amp... if nothing, replace tda2003