Sounds like a grounding problem.
The touch screen is looking for your finger to be at the same voltage as most of the phone (which is at the same voltage as you because you’re holding it).
When you plug the phone in to a charger, the voltage of the phone changes to the “ground” voltage of what the charger is plugged into. Now the screen doesn’t see the phone at the same voltage as your finger and refuses to work. Some chargers are isolated (so the phone doesn’t get grounded) and some are not. The work around is to ground yourself as well!! Touch something that is earthed … like the outside of a metal kettle or the edge of a plugged in laptop, and the screen will work … sometimes your body potential will stay at “ground” and the phone will keep working when you disconnect yourself from ground … sometimes not. It depends what you’re standing on (whether you’re wearing socks … standing on damp ground … all sorts).
Had this endlessly with my old mobile and sometimes withe the FP2. It’s physics sadly.
PS it probably works when charging off your pc because the pc is working off batteries or has an isolated power supply. My Dell laptop isn’t isolated btw so if you use it plugged in, with bare feet you get a buzz off it.