I tried everything in this thread including the reset all settings above. What finally did the trick is a hard reset (ie, Erase All Content and Settings). I did do an iCloud backup before and restore after and that did not affect the touch id, it still worked after the hard reset.
The previous suggestions in this thread will likely fix your problem, but in case they don’t, here’s one more thing to try. I unplugged/replugged the battery and home connectors so many times and it just wasn’t working for me. :)