think that I broke the display circuit

If the home button feels like the phone is on and you didn’t disconnect the screen to work on the home button I bet you damaged a screen ribbon.

Turn the phone off. Disconnect the battery then disconnect everything else. Make sure the home button is seated and connected properly and the plate is fitted. Reconnect the ear speaker flex and the screen and home button connectors then finally the battery then try it. If the home button works and the phone vibrates when you flick the mute switch then I’d say it was a screen issue. If you didn’t disconnect the screen and battery whilst working on the home button I doubt it would cause a back light problem.