Why is my home key not working

Try a Forced Restart on the phone. Follow the instructions very carefully, as this is a bit tricky. You may need to repeat this several times.

Force restart iPhone - Apple Support

There are only 2 possible results when you perform a Forced Restart:

1) The phone returns to normal operation

or else......

2) There has been a hardware failure on the phone that will need attention at the Apple Store (make an appointment) or visit an authorized Apple Service shop

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