Did you also check your Touch ID settings?
Any restrictions set up in Settings/General/Restrictions?
Can you sync with iTunes on your computer?
Did you try to connect via USB when the Lock screen is not active?
Did you check the docking port for any kind of debris or lint?
Does restarting the phone or force restarting the phone by holding the sleep and home button for about 10sec, until the Apple logo comes back, change the situation?