iPhone lcd works perfectly but does not respond to touch

I put my iphone 5c down for 5 minutes, in an otter box case, and it is working fine. I return to my phone and push the home button, the screen lights up and shows me a screen to input my password. so far so good. I try and put my password in and its not receiving any of my touches. No matter how frantically I touch the screen nothing is responding. So i figure its a bad screen, I buy a new one, install it carefully, step by step, turn it on and the screen lights up and I have the exact same problem. I cannot find anyone with a similar issue (maybe I dont know how to use google properly) Does anyone have any ideas?