It's hard to see from the photo, but check for corrosion around the base of those SMD electrolytics. I've repaired many machines on which those capacitors have leaked, which causes corrosion of PCB tracks.
Look for discolouration around the capacitors, solder joints looking "tarnished" instead of smooth and shiny, and a fishy odour which is very strong when you heat the solder joints.
If this is the case, I'd suggest replacing all the SMD electrolytics in the machine, especially all the 22µF ones. There is a couple behind the serial port to replace at the same time.
You'll probably find that some PCB tracks and vias have been corroded and will need repairing.
Find someone who is experienced with SMD soldering to replace the capacitors, as it would be easy to lift tracks and cause further damage if not done correctly.
As for your battery clock problem, check for open circuit tracks around data latch U177, which may require replacement as well. You can get them from decent electronics suppliers, plus I keep a stock of them here if you get stuck.
If you need schematics on this, get them here:
http://amiga.serveftp.netI'm planning to write some web pages on battery replacement and RTC repair very soon when I get some spare hours, so if all else fails, keep an eye on the above site

Anthony.