Sounds like a bad ribbon cable connection between the cable and screen, or cable and motherboard.
Charging generates heat, and apparently just enough to improve the connection. Not sure if the PB cable is connected w/ a removable connector or soldered in place, but if you're up to it you might try opening it up and re-seating the display cable. If that doesn't work you can try running a soldering iron quickly across the ribbon cable to re-flow the connections at each side.
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