How do I fix an unresponsive Home button on my iPad?

Make an appointment at the nearest Apple location to have your iPad evaluated for free.

Once the diagnostics are complete, the staff will explain your options.

Make a Genius Bar Reservation

Genius Bar Reservation and Apple Support Options - Apple

Or use this link to see if Apple can run remote diagnostics on your iPad:

Get Support

If you cannot turn the iPad on, remote diagnostics will not work and you

will have to go to an Apple store or Apple authorized service provider.

It is a common misconception that an iPad (or iPhone) can remain fully functional with damaged or defective physical buttons. 

Whilst Accessibility features (such as assistive touch) can be used to augment the User Interface, these features cannot be used as a substitute for physical button sequences that must be used to trigger system recovery actions. Sooner or later, as now, you will encounter a situation from which you cannot recover.

Until repaired, you will not be able to resolve a locked-out (disabled) iPad - or reset a forgotten device passcode.

You can arrange repair of your iPad either by (a) visiting the Genius Bar at your local Apple Store or Apple Authorised Service Provider (AASP) - or (b) using Apple's mail-in repair service:

Genius Bar Reservation and Apple Support Options - Apple

iPad Repair & Service - Apple Support