I've been working with a repair for an iPad 4 for a few days. It's not my first iPad or Apple repair for that matter. I did however learn something new after the new touchscreen digitizer was unresponsive. After examining the old screen I noticed the small outlining of foam with makes a rectangle around the inside of the screen. I have noticed it before but never needed to investigate because my previous repairs worked. The foam was torn, higher in places, and completely gone from others. I deceided to cut 1mm strips (enough to go around the display) but not before dividing a 2mm rectangle to make it thinner, like cutting a slice of bread to make 2 thin slices. After appling this to the outside of the digitizer contact with double sided red tape the iPad worked like a charm.
If all else fails, you might want to try this. I have already cut all the gray foam that comes with the parts I have ordered in the past, just to ready for the next iPad. Maybe this will solve someone's issues with unresponsive touchscreens like it did mine.