Hello.
I just bought my Lumia 920 and started facing this issue after some MINUTES.
Been reading all the answers over here and trying them, also testing the phone.
Hard and Soft Resets doesn't seem to solve the problem instantly. But when I tried to do so (hard or soft) after some time it worked. And after using it some minutes the screen freezes again. Tried to do it with SIM and without it too. Same thing.
When it is off the charger it takes longer to freezes. It makes me get closer to some hardware issued related to phone heating. Maybe after some heat the board shuts down something related to the touch screen.
It could be a Software issue, but I'm pretty sure that this is HARDWARE related. This makes sense to people telling that turning WiFi off solves it. Turning it off reduces usage and heating too. Reducing number of softwares working background also reduces the processor usage, and heating...
Sure, we just can't stop using all the phone's power just to avoid this issue. The solution is to send it back to Nokia and request a new phone. If this is a Lumia 920's known issue without solution, then, unfortunately it's time to change phone.
Damn... I just bought it... Couldn't even use it...