Edward,
This one had me curious I guess. I went back and looked at some schems and notes.
As you know, the board is pretty simple, CPU boots, loads data from the U3 and U4 proms via U2, with U5 handling OE, outputs data to the DAC at U6 which in turn sends analog to the audio amp section. The rest of the board is support for the cpu and so forth (clock, rst, Vcc, etc.)
That the board outputs audio with the test switch tells a lot. Any fault with the CPU, ROM, DAC or analog circuits should either give you either no audio at any point, or messed up audio both in-game and with the test button.
Just like on the MPU board, the First LED flash might be quick. Very quick. So quick it might be hard to notice. Maybe the board is getting to the fourth and leaves the LED on (wish I had one here to check). If it is the fourth, that's all of them on a Cheap Squeak and the board has correctly booted.
Where's that leave things? Well, there's no sound call input buffer on the Cheap Squeak. Sound calls from the MPU to the Cheap Squeak go directly to P20 - P24 on U1. Since you tried another 6803, we can assume the problem isn't there. That moves the issue off the Cheap Squeak over to the MPU side of things. I thinking the issue is either interconnects/wiring between the boards or an MPU PIA related type issue (I don't have MPU schems handy and I don't recall if there's any logic/decoder in the chain on the MPU or if sound select is right off a PIA)
Good luck!
D