@r_welfare:
Yeah, you should remove the battery ASAP and clean away the stuff that has leaked onto the motherboard so it doesn't eat more of it.
Quotes from
this battery repair guide:
"Obviously the battery needs to be removed. If you simply can't be knackered fixing the computer, the least you should do is remove the battery using a small pair of sidecutters to cut the 3 legs holding it to the motherboard. This will stop further corrosion."
"Using a combination of the toothbrush and rag, clean the visible corrosion damage from the board using the methylated spirits or isopropyl alchohol.
You can scrub quite hard with the toothbrush with little risk of damage. The components and soldering are quite robust."
Btw, the battery is not needed for the Amiga to function, so don't worry too much about replacing it.
Not regarding the battery, but also do not forget to try what I mentioned about pushing the socketed circuits into place as it is often the source of old Amigas not working.
/Patrik