Disconnect the device from it's cord, if plugged in.
Restart your computer.
Conect the iPad to a DIFFERENT USB port and see if there is a change.
If not, disconnect from the computer.
tap Settings > iCloud > Storage & Backup
tap "Back Up Now"
When the back up is finished;
tap Erase All Content And Settings
When the iPad restarts, it will display the Setup Assistant. In the Setup Assistant, temporarily choose to set up as a new device rather than restore a backup. You can skip all optional setup questions as desired. We just want to test the unit in "out of the box" condition right now.
See if it is then recognized by the computer and iTunes.
If it is not recognized, skip the Part 3 and go straight to Part 4.
If it IS recognized
Disconnect from the computer and restore from iCloud and test once more;
then tap “Erase all content and settings”
When the iPhone restarts, it will display the Setup Assistant. In the Setup Assistant, sign in to iCloud, tap “Restore from a Backup,” then choose from a list of your backups in iCloud.
Once finished, see if iTunes still recognizes the device. If it does, you should be good to go, if not then...
The following procedure is a special firmware recovery mode (DFU). It will erase your Apple device, re-install the operating system, and then re-sync user data once it is done (provided you have a backup of some kind).
Make sure you have downloaded and installed the latest version of iTunes on your computer before attempting this:http://www.apple.com/itunes/download/
* Open iTunes on your computer and connect the Apple device directly to it
* Turn off the Apple 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).
* Hold down the sleep/wake button (on the top) AND the home button (on the front) for 10 seconds
* Release the sleep/wake button but CONTINUE to hold the home button, until...
* iTunes should pop up and tell you it’s found a device in recovery mode, click ok and continue along for the restore.
Note: When you are in DFU mode the device's screen will be completely black.
Note #2: it may ask whether you wish to restore a backup from iTunes or from iCloud. You should use iCloud.
If it doesn’t work the 1st time, start from the beginning and try again. If iTunes *still* doesn't recognize the device, plug it into a DIFFERENT USB port and try once more.
If you reach this point and the iPad is still not being recognized and you are unable to complete the DFU mode procedure then you are dealing with a physical issue in the iPad - probably a fault in the Lightning connector port. You can try using a flashlight to make sure there is no foreign matter in the port that might cause issues but this is not usually the case. At this point, you would need service by an Apple authorized service center.