This happened to me once. My issue was that I damaged the cable under the lcd shield that ran to the home button. I could not restore my iphone since it gave me an error 53. I would suggest you to read this as it was helpful on the topic: http://vkrepair.com/iphone-6-error-53/
Did you yank the home button off the old display by the flex cable like people do in youtube videos? If so you probably tore it. Another common failure point is that flex that runs behind the plate will get torn where it attaches to the back of the screen with adhesive
For future reference, use some heat to remove the prox/front camera cable, the home button cable connected to the plate, and the home button cable itself. These are usually the results of not doing it
"I replaced my screen and used the original home button with the new screen. The touch id and the home button were working just fine for three months. Then one day I woke up to the iphone's touch id not working and the battery draining rapidly. Something mysterious happened from the time I went to bed to the time I woke up that caused a fault with the phone. So I don't believe I damaged the ribbon cable. I can't remember if I had done a SW update.
I have a suspicion that a replacement screen can be incompatible and cause the problem. If you read the apple support page for error 53 it says... ""For example, an unauthorized or faulty screen replacement could cause ... error 53""
I find the wording very interesting... So and unauthorized screen replacement in itself can cause the problem! interesting...."
