it sounds like the operating software has crashed during the update. The following should set it right again;
Make sure you have downloaded and installed the latest version of iTunes on your computer before attempting this:
(Mac users can run System Preferences > Software Update (or “Apple Store” for OS X 10.9 users) > Check now to get the latest version for their system in most cases.)
Disconnect all cables from your Apple device.
Open iTunes on the computer
Turn off the device (press the sleep/wake button on the top until you see the red slider and slide the red slider across to the right OR until the device simply shuts off, if locked up).
Press and hold the Home button. While holding the Home button, connect your device to the computer running iTunes. (If your device doesn't turn on automatically, turn it on.)
Continue holding the Home button until you see the Connect to iTunes screen.
iTunes will alert you that it has detected a device in recovery mode. Click OK, then restore the device.
It may ask whether you wish to restore a backup from iTunes or from iCloud. You should use which ever has the latest backup of your personal data.
If you still have concerns, please do not negatively rate my answer, simply reply back before rating. I'll be more than happy to work with you further. When we are finished, please give my answers a positive rating so I will be credited for my assistance. You are judging my personal service only (not this website, the price, or your issue) and high ratings assure I remain in good standing.
Thanks and good luck,