I would start by checking the PSU voltages first at the motherboard connector.
Since you changed the 68000 socket i wonder if a broken or marginal trace is the problem,i would suggesting doing a continuity test on all the traces to make sure none are broken.
Check the kickstart socket too,not uncommon for them to suffer from battery corrosion.
Since the machine was working then got worse,i would pull the coin cell holder and investigate the damage under it. you can stop the corrosion with a cleaning of vinegar followed by iso alcohol.
Last but not least the capacitors are cheap to change and could very well play a part.
any common diode should work for the coin cell such as 1n914, but a Schottky diode has less drop and might be better(1n4148)for max coin life.
