Water damage is tricky because anything can be wrong with it.
1rst step would be to remove the motherboard and cleaning as best as possible with Iso 99% and a brush.
Once most of the corrosion is removed, you could test it again, but there are still many area of the motherboard that you will need to use soldering equipment to access.
Ideally you would inspect all the connector under a microscope to see is any of the pins are corrored away from their pads and move on from there with more troubleshooting and testing.
From the sounds of it, the circuit board has at least one short inside of it hence the heat you feel when trying yo charge it, so replacing the screen is propably not going to do you any good at this point.
A quick and easy test that you could do is grab a multi meter and place it in diode mode.
Disconect the battery, and put the leads on each end of the battery connector on the motherboard.
One orientation should read 0.4V, and if you switch the leads orientation on the connector you should get 1.2V. If you get 0.4V in both orientations then you have a short on VCC_Main, and it will need to be resolved before replacing any parts like a screen for exemple.