Chosen Solution
After a successful replacement of the glass on an iPad mini 3, the undamaged home button is not functioning when pressed. There are no errors reported on start-up. Given these circumstances, does this mean the connector on the logic board has been damaged? Again there are no signs of damage that I can detect.
Assuming you don’t have a teeny microtear in the flex then the MOST LIKELY problem is a parts problem on the screen. These are notoriously bad. Definitely make sure to test home button function before sealing it up.