I was brought an iPad 2 today that was on and running, but for some reason the power and home buttons were not working right. Pressing or holding the power button did nothing. Hitting the home button would not take you back to the desktop, but oddly enough it seemed to take you back a screen in the settings page. So it seemed that the Home button was still functioning at some level.
Searched the internet and found that this has happened on many iPads. One person suggested to hold the Home button, then rotate the tablet from portrait to landscape mode. Though it seemed to work for many people, it did nothing on this one.
Finally I had to hit and hold both the Power and Home buttons for like 15 seconds and the unit finally returned to the desktop. I hit the Home button twice to see what was running. There were about 20 programs open!
I closed them all and rebooted the iPad.