Thanks for the floppy tip. The drive that came with it wasn't doing much of anything on power up, no spin, no light, just one faint click.
I _think_ I've made some progress. Here's what I've done so far:
Removed the slightly fuzzy battery and soldered some wires to the motherboard for adding a replacement battery (later). Cleaned the board. There didn't seem to be any significant damage to the traces or any nearby components.
Removed, cleaned and reseated every socketed IC.
Took an old PC floppy drive and made the mods suggested on this forum.
Hooked up just the power supply, motherboard, floppy drive & keyboard.
If I power it on with no floppy inserted, the power LED is bright, the floppy drive clicks about once every 2 seconds, the caps lock key "works" (i.e. switches the caps lock light on and off), no video on the composite output.
If I then insert a disk (don't have a workbench disk - this is just a grub boot disk for PC) the floppy LED lights & blinks twice while clicking (trying to read?) then stops - no further activity from the system.
If I power it on with the grub boot disk inserted, the floppy led lights, clicks & blinks about 5 times, then stops. Caps lock light on the keyboard then blinks. No video out on composite.
Is there any point to hooking up the audio output? Does the amiga use any sound during post to indicate errors?
Does anyone have any thoughts on the next troubleshooting steps?