Had the same problem. My iPhone (iOS 9.3.3) asked me to enter my six digit pin to enable touch ID, which was a bit strange itself because the phone hadn't been switched off. I entered my passcode, as I have done several times before but it was rejected. I always write down my passcodes and tried using older passcodes as well but none of them worked. Ended up getting locked out and only getting an attempt every 60 minutes.
Based on what Lord Lethris said above, I restarted the phone and reverted to trying my most recent passcode. Finally, it accepted the passcode.
It then took a long time to restart and I saw the progress bar and Apple logo on the screen.
Then, it went to the welcome screen and asked me to select a language. That was incredibly frustrating as my last iTunes backup was over a year ago. I selected English and then it told me that was phone was linked to an Apple ID. I entered my Apple password and, as I was out for dinner I just left it in my pocket and looked at it a couple of hours later and suddenly it had been restored. I think that came from an iCloud backup which I now consider to be 99cents a month very well spent.
Ended up having to go through a whole process of resetting passwords and security questions as well. Incredibly frustrating but it seems that iCloud is backing it up every day which was a huge relief.