Iphone 6 screen selectively responsive

Yesterday at about 2 pm my screen just stopped responding, it randomly starts functioning for a few seconds, then goes back to not working. I don't think I dropped it because it was working all day yesterday. I've soft reset, hard reset, done a DFU restore, nothing has worked. I don't think I have the "disease" because there's not grey bar at the top of the screen, the whole screen looks completely fine. Any ideas as to how to fix this?