Koaftder,
Yes, there is an A3000 service manual available. They show up from time to time on eBay (look for merchant Centsible Software) or you might contact Software Hut and ask to buy or get a copy of the manual. There is a copy of this manual on
eBay right now.
You comments about the various problems is not unexpected given the age of the parts you have. The single worst item was the battery. I'm glad you removed it. Be sure that all corrosion is gone from that area!
Something else that would be of great use to you would be a product called "Amiga Analyzer" which was a hardware / software test kit used to diagnose many problems on the A2000-A4000 series using WB2 or 3.1. If you can find one of these it will be most useful to you in repairing your old A3000.
Good luck,
Regards,
Ltstanfo