Touchscreen issue have many origins. This week someone that contacted my heaven had her issue solved by a factory reset. Yours appears to be hardware issues.
If you know another FP2 user or if you are near a FP angels’ heaven you should try swapping the screen modules. If this solves the issue then your module is probably the problem and you can buy a replacement.
Still the touchscreen working partially suggests a problem with the connectors. You should try to clean them. Read here: