When debugging a Williams Gorgar sound(no sound out at all), I discovered that the voltage coming from the transformer at that tap is ~9.4V. According to the schematics I have, that should be 18.7V AC. So, I'm assuming that this is likely the root cause of my problem.
Since the rest of the system seems to power up just fine, I'm inclined to simply replace this particular voltage, with a separate AC transformer. Has anyone else tried this?

Looking at page six of the manual(the block diagram): http://www.ipdb.org/files/1062/Gorgar_Manual.pdf
It shows that the input to the sound board is 18.7V AC. I have also traced those wires back to the transformer directly. The logic is not connected, AFAICT.

Right. I posted that as I didn't see a connection to the 12V logic supply.

I think I made some bad contact when I was measuring the power originally. This time, I got a clear 19V from the incoming voltage.
I got +12V,-12V and 5V on the test points.

I'll run through the rest of the debugging and see where I get. I've already ruled out the front volume control.

Ok, so it wasn't voltage. Mysteriously, the sounds(but not speech) have started working. Now I'm going to work on narrowing down the cause. Thanks for the posts!