Have you tried a hard reset? Press the home and on/off button together until you see the apple logo and let go. if that doesn't work try applying some pressure to the top right of your screen. That is where the digitizer connection is located, in some cases a well placed squeeze may fix the problem. Also before ordering the part open the phone according to the guide on ifixit and check if your digitizer cable is installed correctly. Then reboot the phone, no response? Hard reset, still no response? Replace the part.
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