I had the same problem. But I got it fixed. The 3D Touch and home button cable (one cable) is very fragile. Remove the metal backplate on the back of the screen an check the complete cable. Mine was broken. I replace the whole backlight + 3D Touch (Removing of the old backlight + 3D Touch is very hard) and the Touch ID is working without any problems.
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If you have any questions feel free to write me a message.