That would require additional hardware that you usually won’t have, but you could try to charge the battery outside the phone. Perhaps there is something wrong with the control circuits (Li-ions need control circuits to prevent overheating/overcharging) in the phone but the battery is still fine.
Something like this:
I have no experience myself with any of these chargers, I just wanted to add this piece of advise. Perhaps the battery could be charged normally once a certain base level of charging is done.