Il Mio Problema
I did a screen repair on my own iPhone 6 plus a few weeks ago and everything went fine, except for that the Touch ID was no longer working. This was until I tried to update the software on the phone and essentially bricked it, giving me error 53 whenever I plugged in the phone. Through some research on the internet I found that this is a common problem when messing with the touch ID or home cable. I was banking on the long cable in the back being the problem as that was the only part of the screen repair that gave me trouble.
La Mia Riparazione
Extremely easy repair, just took the screen off the phone and replaced the metal back plate. It was just a bunch of screws, disconnecting all the cables for the display and disconnecting the home button. Took less than half an hour, ~20 minutes to complete. The part came in very high quality packaging and everything works good as new now!
Il Mio Consiglio
If you are doing a screen replacement on a 6+ be EXTREMELY gentle with the home button cable. I was lucky that it was just the long home button cable and not the cable on the home button itself. If you are getting error 53 and it's due to the home button being broken you might just be SOL, as your touch ID will never work again as the home button is linked to the logic board or something along those lines. But if it's the long cable in the back Touch ID will work good as new when replaced and Error 53 will go away.
On a side note I've noticed on the 6 and 6+ the home button cables are connected with an adhesive and they are quite hard to get off the plastic, be patient when dealing with these cables otherwise you can and will break it!