How to continue with upgrade when the home button is not working?

So you are hitting the home and on/off buttons to reset, and it boots up to that message, correct? That’s good, since the home button is clearly functioning and we know this is a software problem. (If it was not functioning it would not work to turn off your phone).

• If your iPhone's operating system malfunctions to the point that it looks irreparable, you can try to put your iPhone into DFU (or Device Firmware Update) mode to update or restore the device.
• You can resurrect your iPhone by downloading a new operating system with your phone in DFU mode, though this will delete your phone's memory. You have backups, though, so at least your data is safe.
• The process can be tricky, so be prepared to try it several times before it succeeds.