Try doing a reset of the iPad. Here's the process:
Reset: Hold both the power and home buttons until the screen goes dark and the Apple logo then appears (the slide to unlock screen may or may not appear). Once the logo appears, release the buttons. After a time, your homescreen will appear. Please note that it may take some time for the Apple logo to appear or for your homescreen to appear (or both). This is normal. Eventually, the homescreen will appear.
If that doesn't solve the problem, I'm afraid that, given your description of a pressed in sleep button, that you'll need to take the iPad to the Apple store for them to look at it. It might be that you have a hardware problem that may be easily fixed by the Apple geniuses.
Sorry, but that's all the suggestions I can think of.
Good luck and let us know how you get on.
Marilyn