Have you tried restoring your iPad. You might also want to try this.
1) Go into a stock iPad app (i.e. pre-installed ones) for example the Calender or Notes.
2) Hold the top power button down until you get a message to slide across to power off and then let go of the power button.
3) Now hold the home button down, keep holding it and eventually you should go back to your home screen.
Try using your home button now. What that does is re-calibrates the home button and may solve your problem. After I jailbroke my iPad my Home button become very unresponsive and that sorted it out for me. If that doesn't work then I'd recommend swapping the iPad over as it probably is a hardware issue.