I had this same issue while repairing an iPhone 5C screen. Screen worked great when tested but when I put the plate on to cover the connections and put it back together, it would not respond to touch. After a little trouble shooting I put the phone back together and just left the connector cover off and it worked.
Seems to be an issue with the connector plate contacting the connections and shorting them out. I solved the issue by transferring the black foam connector pads from the broken screen to the new one; wa-la.
Hope this helps someone.