I also had this problem. It looked just like the video posted above. I tried many of the suggestions I saw on the web but nothing quite worked. I finally broke down and I took the phone in and had the screen replaced.
$105 @ Bulbs and Batteries store.
I guess they have 10% off if you schedule the repair online which I didn't do.
The tech there was very good at analyzing what the potential problems could be.
He seemed to say that likely power was not getting to the screen in sufficient quantity to keep the screen fully powered.
It could be as simple as a loose cable if the phone was dropped, some water damage even though I detected none when I looked at the water damage dot in the SIM card slot., it could be that the screen was going bad and not getting enough power, or that somehow the mainboard was damaged and not supplying enough power to keep the screen going.
He thought it most likely to be from some sort of water damage or damage to a cable connecting the screen. Possibly a drop or even some moisture had gotten into the phone from something.
He said that probably what was happening was when the phone was initially turned on it was fully functioning as it should but due to loss of power or decreased power to the screen.... the screen would dim and when the power was not sufficient, the screen froze with just the last input image which is why it couldn't receive any finger input. Essentially what was left on the screen was an image of the last thing which was happening. Enough power to see that, but not enough for any input or swiping because the screen was only displaying a ghost image essentially
The screen replacement took only an hour after I dropped it off. They said there was water damage, but only to one of the components being replaced during the screen replacement. I was lucky in this case.
The phone so far is fine.
Good things about taking it to the shop.
1. tech experience in analyzing the causes of iPhone malfunctions
2. fairly inexpensive screen replacement. Screen ~$60 bucks. 45 for service which is reasonable given the time and analysis.
3. I couldn't inadvertently damage the phone. I have fixed several iPhones before, but at some point I could brick one. Usually I only do cracked screens cause I know they are the culprit.
4. I have a 6 month warranty on the phone screen. If anything should go wrong with it I can bring it in for another replacement.