How do I restore unresponsive ipad?
since assistive touch is still working you can shut down the iPad through that.


Locate your “Assistive Icon” and tap on it
An option of ‘Device’ will appear along with other options.
Tap on ‘Device’
You will see ‘Lock Screen’ icon. Press and Hold this option for a while. 
After a few seconds, the power off screen will be displayed.
Slide it to switch off your iPad.


When it is off you will need to plug it into a charger to turn it on again or plug it into itunes to restore it