What components typically need replacement after water damage?

This is not just battery issue - problem is with charging port -connector itself is definitely corroded and in most cases should be replaced. Further on you will have to pull out Motherboard and inspect water damage. try with Alcohol and tooth brush very gently remove corrosion. If this will not help try to locate damaged filters and capacitors around battery connector - different colour of others (dark, black) of contacts is very good indicator that should be replaced. With microscope and a bit adventure in your blood you can start micro soldering process or maybe find somebody who are dealing with this kind of repair. water damage is very common problem so I think that you will not have a big problem to find somebody .