Well, at least you know the problem is with the expansion.
It doesn't look badly damaged. You could try the following:
Check the condition of the pins on the ram expansion bay (on the Amiga) for any green corrosion. If so you may need to clean them.
[Its possible that the acid from the battery ran from the tracks through to the pins, in bad cases it can even travel to the motherboard itself.]
Check the ram expansion with a digital multimeter for continuity - You will need to check around the area that got damaged / corrosion from point to point. If there are any breaks in the tracks you will need to repair them. Bridging them or whatever.
512K ram expansions are cheap, so if you cant fix it its no big deal but i'm pretty sure its fixable.
