Hi Alex!
Oh my... The only thing you can do is to clean it with isopropryl alcohol. The whole motherboard, but this is what you already did.
So, the next step is to replace the battery pins for new ones! Soldering is required, but it's not that difficult.
If that didn't worked, then there is something (or more things..) damaged on the motherboard. If this is the case, it's probably not worth to repair it. Sorry.
Hopefully replacing the battery pins will do it!