A dreaded gray bar
The repair community were the first to identify a problem with some of Apples iPhones, and they named it "touch disease." We've seen it in the iPhone 6 and 6 plus. The symptoms are a screen that doesn't respond to touch, or responds intermittently. Often there is a gray bar at the top of the screen. Unfortunately a screen replacement won't fix this. It is a problem on the logic board and requires microsoldering to correct it.
What causes it?
It is caused by the logic board flexing, either during a drop or by being in a back pocket, or by another stressor. There are microchips on the logic board (the brain) of the iPhone that become dislodged.
Can you fix it?
We can send the iPhone to a repair partner that has the specialized tools to do this repair. At the time of this writing, Apple is now offering to fix the 6 plus for $149., but admits no fault in manufacturing. And they won't fix the iPhone 6 for that price, they'll charge you $299. This is cheaper than their out of warranty fee of $329. Class action suits are pending.