This afternoon, after about 3 weeks of working fine, the Home button (the one on the face wth the little circle) stopped working! Very frustrating. I found out on the web that this is a fairly common problem. I've tried all the suggestions here.

Will Apple replace the iPad or repair it?

Same problem happened to me, what I did reset my iPad and then started works.

If your OS is 5.1 go to settings > general > Assestive Touch, enable it ON then you will get a virtual home bottom on your iPad screen use it to avoid multi use of visical one.

Or you can also use the multi gesture instead (use five fingers to return to home screen or pop up the recently opened apps bar)

Just in case this isn't one of the things you tried.

How To: Recalibrate Your iDevice's Home Button -- AppAdvice

Been having a problem with mine will try this