This has been mentioned before, but I’m still posting this as new since I had missed the trick before, and this could extend the life to a phone or display that might be heading for recycling otherwise, for almost free.
Trying this will void your warranty and can irreversably destroy your display. Only do this if you are sure.
So I got the dreaded non-responsive touch screen problem on my FP2. Left side of the screen had a vertical stripe that didn’t work. As the phone is getting quite old I considered my choices for quite a while. After a lot of deliberation I decided to order a new screen, but then I stumbled on stories and videos on using the igniter from an electronic lighter to revive a touch screen. It sounded unbelievable, but since I had nothing to lose I dug up an empty lighter (the fireplace type with a long nose) and tested it on the touch screen without even bothering to strip the igniter out of the lighter. Lo and behold, my touch screen was back in action! Some say the problem may recur after only a few days or even less (and someone said they carry an ignitor with them at all times), but I’ve been lucky since it’s been now working fine since 16 July.