I would focus on the backlight driver ic which is a small 9 pin BGA just above the connecting ribbon between the two boards. Normally part number starts with a U. This can be easily damaged with poor fitting of ribbon connector and may be triggering the two issues you describe above. The same part is used on the full Switch if you can rob one from another board, or I’ve found that a TI TPS61163A is a suitable replacement.
Good luck! Sheriff