Just wanted to make the effort to thank those involved in this thread.

I'd spotted the blown capacitors myself and replaced them, but the clicking continued, and I was on the verge of assuming that something further down had blown as well.
Advice on resetting the eeprom worked exactly as described - took about fifty attempts over an hour or so, but eventually the backlight popped on and I got into the service menu. I might have given up earlier had the advice on this topic not been so specific.
For resetting the eeprom, I used long wires and soldered them to the legs of the eeprom chip. From the discussion on the board it sounded like they would be super tiny connections, but they weren't all that scary when I got the AV board over. Needed to get the magnifying glass out, but that's more to do with my eyes! :)
Anyhow, thanks all. I don't know if the fix will last, but this ressurection was a fun little project.