Well I had the same issue with my iPad. here is what I did to resolve it in within couple of hours.
Plug iPad into wall socket charger and keep it for at least 45 mins. This would ensure it has enough charge to do multiple reboots in the recovery/restoration process.
FORCE IPAD INTO RECOVERY MODE using the below steps:
Note: Ensure your iTunes is latest if not just update it. Should not take more than 15 mins on a good connection.
1. Turn on computer/laptop and launch iTunes (make sure you use the latest version of iTunes)
2. Plug USB cable of iPad into the USB port
3. Hold Home button down and plug the other end of cable into docking port. Do not release button until you see picture of iTunes and plug.
4. Release Home button.
ON PC/Laptop
5. iTune detects iPad in recovery mode (you might get a notification of drivers being installed in the right corner for the USB Device connected; just let it complete).
6. iTunes will now detect iPad and ask for Restore & Update. Select "Restore iPad"
7. iTunes will download the latest Software for the iPad and this could take anywhere between 30 to 60 mins. You can disconnect your iPad after 10 mins and plug it back to the socket charger for charging. Reconnect iPad 2 mins before the download completes using steps 2 to 4.
8. Follow the Restoration steps and do not disconnect iPad before it gets completed.
9. Once the restoration completes it will take your through the completion process on iPad, just follow steps quickly.
10. Put iPad back on the charging through wall socket charger and confirm it is charging.
11. Now turn off the iPad and let it charge for a sometime.
I hope this fixes your issue and that you are able to use your iPad just like I am able to now.