If something is not working right, restarting or resetting iPad will likely solve the issue.
See these support articles:
iPad: Turning on/off and resetting, http://support.apple.com/kb/HT4057
iPad: Basic Troubleshooting, http://support.apple.com/kb/TS3274
iPad: Troubleshooting touchscreen response, http://support.apple.com/kb/TS3293
Thanks for the links, Jim. (I've marked as "helpful.")
Unfortunately, I've tried these steps. In fact, I often need to reset my iPad just to wake it now, as I've described under a separate topic...
Looks like I need to bring it in to an Apple store.
The screen on my ipad2 was unresponsive. I could not slide to turn it on nor could I slide to turn it off. I rebooted by pressing and holding both the home and the on/off buttons until the apple logo appeared. After it rebooted the problem was still there. I then made the ipad go into DFU mode and reset to factory settings and restored my ipad. The problem was still there. I took my ipad into an apple store and the "genius" said that it was a hardware problem with the touch screen. He have me a new ipad and the problem was solved.