Managed to get it nicely dusted off. Turns out to have been a bit more dust that I initially thought in some areas. What I noticed was:
1) The top PCB has two black wires permanently soldered in, I think they run to the front panel, probably common? The bottom PCB has one red wire, probably the +6 V line, also soldered in. Because of this neither board can be fully removed, and it took a bit of careful positioning to dust them off.
2) One of the wires on the J3 top to J3 bottom wiring loom wasn't crimped properly! I'd disconnected it from the top board, and then noticed the end at the bottom board was wiggling free. Luckily it appears to be a ground line - there are multiple on that loom. I forgot to check the bottom board, but that end might not even be connected.
3) Rifa caps. The X and Y capacitors are Rifas. Should I replace these?
Cleaning took longer than I expected, but I did manage to probe all the voltage points listed in the service guide. All were within specs. And halfway though that the unit started working again. I turned it off after probing the points on the top board, and it powered up fine when I was about to start on the bottom.
If it's not a power supply problem, maybe it's logic?