I was having this issue on one of my 920s. Thought it was a lost cause until I rebooted it again after a couple months.. The touch screen now works...
So then I tried to set it up using an old backup with my sim inside the phone and then it locked up again. I took out the sim and soft reset it, surprisingly it started working again. So then I decided to hard reset and chose to start fresh without using a backup. Put my sim inside and it didn't become unresponsive!
I have a feeling this is software related and is somehow triggered when you have a working sim inside the phone.. Might be that in conjunction with faulty apps but who knows..
For people facing this issue, take your sim out, Soft reset the phone (Hold Vol Up + Power until vibration) and see if the screen works again. Just a hunch but I think it will work.. If it doesn't then leave the phone off without a sim for a few days and boot it up to see if its working. All these are just hunches that I've made from my own observations so take it with a grain of salt.