So, I'm having this problem and haven't been able to resolve it:
- replaced iPhone 6 LCD Screen & Digitizer (iFixit parts); Touch ID failed after reassembly
- cleaned and checked all connections, rebooted phone, erased and restored phone via iOS and then iTunes erase and restore...no luck
- replaced iPhone 6 LCD Shield Plate w Home Cable...no improvement
- ran iOS 10.2.1 update...no improvement
And, yes, I'm using the original home button and ensured the metal conductive plate transferred with the extension cable.
So, I'm out about $85 now and have no Touch ID. The $110 to pay Apple seems like a bargain now.