This look suspiciously like something on my A4000D motherboard..
Story: the clock on my A4000D doesn't tick, and all around the RTC circuit is a thin film which I had assumed to be from the old battery (long replaced). The area is also populated by lots of capacitors like those in the photos.. The machine used to work fine after one reboot but hasn't for some time now.
A few nights ago, prompted by just-amiga users, I had another look at it. A quick look with my new multimeter (took me years to get around to buying one, but it's invaluable! Everyone should get one if they deal with computers!) showed that the traces I thought were bad, were actually fine! No obvious circuit breaks anywhere.
So, I had a little play around - there's actually a variable capacitor on there, and after a little playing I found that one turn anti-clockwise got the machine working at least on some boots.
Now, reading that webpage and seeing the similarities, noting that changing a VC made some difference, and that the machine used to work after a warm boot (slow charging caps?) I think we might have discovered the root problem my A4000 has!
To sum up, I think this problem may well be affecting some Amigas. But, unlike the battery problem, capacitors don't leak acid and ruin the machine totally (at least, I hope not..)so this is ultimately repairable. Hmm, I wonder how many Amigas have been landfilled with a problem which is repairable? Doesn't bare thinking about.