Had this problem on my first iPhone 6 repair.
The problem is that you phone does not detect your home button. There is an IC-chip on it which has the ID and touch config that works SPECIFICALLY with your phone. Behind the shielding plate is a bridge cable that goes from the Home-button to the top where it is connected. If this is damaged it needs to be replaced. Now next to the homebutton is where this bridge is connected to it. If the flext TO the home button is damaged, you need to replace the homebutton. If this homebutton flex cable is damaged you have lost your touch ID forever.
Error 53 has nothing to do with screen change. Home-button and the screen does not communicate with each other really. It Is your phone that does not detect the Home Button that is all.
My problem with this phone i fixed for a friend is that i had not seated the connection between the home button flex to the bridge flex. I opened the phone, de-attached everything and re-attached it again. After booting up it finally restored the iPhone and Error 53 was no more.
Try this if a tech has replaced your screen. That tiny little connection is small and fiddly. Try some rubbing alcohol to clean them if you can. Follow ifixit guides to dismantle or give it back to your tech to recheck the connections.
DFU did not work. It will simply kick you out of DFU and go back to the restore process.