Chosen Solution

The touch screen still works perfectly, but I’m getting no functionality from the Home button at all. I can’t end an app without powering down and restarting the iPad.

well i mean, the most likely scenario is that you need a home button replacement, but before going through the labor, do a settings reset first. if that doesnt work, move on to the replacement.

iPad Mini Home button Replacement This is the replacement guide. pretty simple as far as soldering goes.