I'm repeating myself maybe but you *need* to remove that battery no matter what. It has failed anyway and won't supply the real-time clock any longer - a fact that one can easily live without, it's really all it ever did.
So please go and clip away that battery.
The green/cyan-tinted and/or dull-looking metal pins indicated in the picture show the damage done by the electrolyte that leaked from the battery. It's the opposite of acid but not a bit better in what it's doing. You can neutralize the alkaline with vinegar. If you do, you will observe a reaction, the solution will start producing bubbles. Only when that has stopped, the aklakine was neutralized. It should then be washed away with water to ensure that the vinegar acid isn't causing the next damage. You can actually soak the entire board in water as long as you can ensure that it is completely (!) dry until it is powered on the next time. That is, even beneath the chips there must not be the smallest amount of water left.
After that, it's time to replace whatever was fatally damaged by the alkaline. I'm seeing at least two sockets that need replacement, Gary's socket in any case as it needs all of its contacts, but the Paula socket (top of the picture, partially visible) is also affected. All the places highlighted in orange need to be cured, and probably more around the battery.
You may find that it is hard to melt the solder that got in touch with the alkaline. That's because the chemical reaction between both causes the metal to dissolve into a non-conductive oxide powder. So it is recommended to check all soldering for places that need re-soldering. Also there are several vias (the small "eyes" connecting traces between the top and bottom layers). Be aware that these are just little copper "tunnels" that might have become eaten away so there is no conductivity left. So if the cleanup, socket replacement, and resoldering does not bring back your Amiga, it might be time to check all the traces in the affected area for conductivity. There is a redesign of the board but many things about it are identical to the original A500+ board so you might find some help in using KiCad to see where traces are expected to go:
https://github.com/SukkoPera/Raemixx500.gitHere's another address where you can interactively view the A500 board in any detail in your browser - no other software needed:
https://www.amigapcb.org/Hope this helps!
Cheers,
Joe
