March 25, 2017 - I was having the same issue and here is how I fixed it:
-The Issue: The bottom part of my screen was not responding to touch. The bottom row of the keyboard was not working either. It worked when I tilted the screen.
-Solutions that did not work for me: a) Hard resent by pushing home and power buttons at the same time, b) Resetting all the settings, c) Restoring phone to factory settings and deleting all data. d) Updating itunes and trying to update and restore the software, and e) I took my phone to apple store and I was told that I have two options: either replace the phone with a new iphone 6 for $299 or replace the screen for $120, without any guarantee that replacing the screen would work.
-What fixed the problem? I took my to a local phone repair kiosk and I was told that they will replace the screen for $60 if it works and $0 if it doesn't work. I said okay and 30 minutes later the problem was solved by the screen replacement.