LOL - replacing a part on a water damaged machine and thinking it will "work perfectly fine", is fine if your name is Pollyanna. It's a possibility at best ;-)
I'm sorry I couldn't give you a better answer but water damaged machines can be anything and everything. Your battery has run all the way down and it appears it will not charge.
Here's what Apple says:
"If you see a battery icon appear on the screen instead of an Apple logo, it means the battery in your notebook Mac is too low to start up. Connect the power adapter to charge your Mac's battery, then try starting up again."
You can try a new DC-In board first and/or get a used battery so it will at least boot up and you can run diagnostics.
So far my luck with liquid damaged machines has been hit and miss. There are to many variables involved to give you a definitive fix. It's how much liquid, where it entered, how long it sat there, did it get to the logic board, is there corrosion on the board. If it entered from the keyboard you have a much better change it did not get to the logic board as the newer machines are much better protected on the underside of the keyboard. i have fixed them with just a keyboard replacement,