First up is a B2000, rev 4.1 motherboard. Symptoms are black screen. When pushed on MB around Agnus, ROM, 68k, the Amiga either boots or shows a green screen.
Initial diagnose: Faulty Agnus(socket), bad PCB traces.
Swapping the Agnus did not result in an improvement. Looking at the board resulted in a couple of observations:
1) The board has had a 1 MB Agnus modification
2) Someone didn't really understand those instructions and also pulled pin 41 of the Agnus socket (only needed on A500 models).
3) There was a big scratch running through 2 traces between ROM and 68k.
I couldn't really test the continuity of these traces, so I just scraped, cleaned and retinned them to see if that worked. If so, I would solder a copper wire on top of it and recoat it.
Here also no improvement on the symptoms.
Then I went ahead to replace the Agnus socket. Too bad I seemed to have run out of them, so i'm waiting for replacements.
Hopefully some better news next time.