The LCD appears to have fine damage--(can't see it) separation of the glass LCD when they come usually as a unit can cause this. Have seen this before, there should not be any board damage unless noted during original drop to cause break to begin with-otherwise double check for the slightest amount of debris in the connection.
believing you disconnected the battery and did not cause any damage to the connections -try another screen. also if your old screen worked but was cracked reconnect it to ensure the connections work and no damage to board
was this phone in water by any chance-there isn't a simple part to change if it is over heating there is a short on the logic board-this requires someone that can microsolder to inspect for damage. The battery was replaced so I am going with components knocked of by the battery connection when it was pried out. take a picture of the battery connection.
did you ultrasonic clean the board and do a full inspection for corrosion. Your repair sounds like there is a battery /power problem that needs troubleshooting to start. Water damaged phones are finicky-