Hi, I had this problem as well. My TouchID wouldn't work, and I couldn't even register a new fingerprint. I saw Sherm's answer (it is posted earlier, but I will paste it here for ease of use):
"Ok guys looks like a reset is required of holding down the home button and on/off button for 3-4 seconds. After that the Touch ID works and will allow new scans to be registered."
I would like to add to the above, that when screen goes off, you have to let go of all buttons and press the power button as if you want to turn it on again.
It is now working, but I'm not sure if it's going to keep working, as prior to total meltdown of my TouchID, I could register the fingerprint, only to lose the functionality shortly after. So as much as I would like to be optimistic, the frustration I experienced the last few days is pushing me to pessimism.