Reset the device seems to be the main option, since it's more likely a software issue.
Note: This will remove all the data inside the unit.
With ITunes open
Leave the cable plugged into the computer and disconnect the other end from the phone.
Shut off the device
-If this cannot be done, do a restart by pressing the power button and home button at the same time.
Once the unit is off hold down the home button and plug the usb into the phone.
That should trigger the restoration process (Itunes and USB Logo should appear after plugging the usb). Restore and update the phone to most current OS.
Hope this helps