You will need to rule out the screen as it may be faulty. If the screen is not the problem it will be a logic board problem.
The touch power and data lines are on the bottom layer of the board and are connected to the top half of the board through solder balls. If the phone has been dropped in the past it could have caused one or more solder balls to crack.
To diagnose your problem once you have determined it’s not the screen would be to take measurements of the connector pins with a multimeter and check against the board view schematics.