This has worked for me and others who had the same problem after updating to iOS 5, but there's no guarantee. It's worth a try, though!
Be sure to have the latest version of iTunes installed on your computer before you start.
Launch iTunes, then:
1. Hold down the home button and the sleep/wake (power) button on the iPad at the same time for 10 seconds. Ignore the red power-off slider if it appears.
2. Release the sleep/wake (power) button, but continue to hold the home button down for 15 seconds longer.
3. The iPad will go black.
4. With iTunes open, connect the iPad to your computer with the USB cable.
5. The Apple logo should appear on your iPad.
6. iTunes may take a few seconds to recognize the iPad, but it should do so eventually.
7. You may see the beachball (or hourglass if you use Windows) before iTunes recognizes the iPad, but don't give up and don't force quit unless it goes on for more than a few minutes.
8. Once iTunes recognizes the iPad, it should offer you the option to restore it. If the contents of your iPad appear to be OK as they are, you may not need to restore.
Good luck!