Wish I had an oscilloscope so I could follow along. First of all, since both boards are acting up, you might want to recheck the incoming -12V (-14, whatever) to make sure it hasn't disappeared. Not sure what would happen to the op-amps, but U11 (the DAC 1408) swings negative on its output (Io) and having no power to (Vee) would probably silence it.
You can also look for digital data going from the PIA to the 1408. The 1408 has no "enable" line, so the 8 bit output at PA0-PA7 is continuously dedicated to the DAC, and there will only be bursts of activity (swinging roughly 0V-5V) when the drums are playing.
I'm a little flaky on the transistor circuit around Q1 but I think it's supposed to change the D/A output to swing positive. Assuming you have both 5V and -12V available and data is flowing into the 1408, if the output at pin 4 is dead I would consider pulling Q1 and checking it for a short circuit. If I follow you correctly, you already did that, but if not that's a possibility.
While Q1 is out of the board you can add a load to the 1408 output (say a 510 ohm resistor from pin 4 to ground) and see if you get a small signal across that load.