Always possible the ROM went bad, but the only ways to check that for sure are either to swap in a good one or put it in a burner and verify it.
To really dig into the sound boards, you'd need the diagnostic eprom chip which will test out the ram, pia and CPU chip. There's a number of things which can kill the sound board in the way you're describing, and it's easy to just keep throwing parts until it's fixed. The MC6808 and the MC6821 are both the same chips as used in your main CPU board, so you can always swap them (Assuming they are in sockets).
There are a couple spots you can check with just a logic probe. Power it up, hit the test button, and check pins 2-9 on the PIA chip with your probe, you should see pulsing on those pins if the software is running at all. If they are all solid high, or solid low, the problem is somewhere in the CPU circuit. If they are pulsing, the problem is downstream either in the DAC, the op-amps in the speech board, or in the audio amp circuit.
You can also try pulling the speech board, installing the jumper at W1, and testing again. This will isolate it between the two boards there.
-Hans