Quit the camera app completely again and reboot the iPad.
Go to the home screen first by tapping the home button. Double tap the home button and the recents tray will appear with all of your recent apps displayed at the bottom. Tap and hold down on any app icon until it begins to wiggle. Tap the minus sign in the upper left corner of the app that you want to close. Tap the home button or anywhere above the task bar.
Reboot the iPad by holding down on the sleep and home buttons at the same time for about 10-15 seconds until the Apple Logo appears - ignore the red slider if it appears on the screen - let go of the buttons. Let the iPad start up.
If that doesn't work, you might want to consider resetting all settings and if that fails, restore the iPad iOS software and should that fail, a trip to an Apple Store would probably be in order.iPad (3rd gen) Wi-Fi, iOS 6.1.3, 64 GB
I had this same problem until 15mins ago, i did all the reboot stuff And nothing worked. Then i decided to elimate all other camera apps like Night camera, and the camera began to work immediately. Maybe this will help you too. You can also try to charge The ipad overnight but making it discharge completely before. This also worked for me once with the update to iOS 6.01. Good Luck