You should get touch id back as long as it's the same home button and same logic board they should still be paired. And yes make sure your first step after your home button is disconnected is to unplug the battery.
First I would start with a new battery. While you have it open check for any water damage. Next I would have the logic board tested. Definitely back up everything if you can Update (02/04/2018): What about the connectors on the logic. If you get something to magnify them so you can see better do they look okay. It can get very frustrating some times but what i would do is buy another one from a online app like (Craigs list) or (offer up) that either is locked or has a broken screen so it's cheap but you know it still boots fine. Just make sure you check the IMEI online or call the carrier with the info so you know it's not stolen. Then I would start swapping parts one by one. I have a feeling though that if you have swapped batteries multiple times and tried to restore it that your have some kind of a software defect or something with that logic board has been damaged. What was going on with it when this first stared. Did it just happen one day or were you updating it and the battery died maybe?
That's possible i would try a different battery if you have one and then go to the flex cable. Usually you can see the damage to that unless it's one of the contacts. If neither work than you might have damaged your logic board.
I know with my daughter's kindle fire 5th gen you hold down the power button tell it turns off. Approximately 20 sec. Once it's off all the way hold the power button and volume down button at the same time. As soon as the amazon emblem pops up let go of the power button only make sure your still holding the volume down button. After a couple seconds let go of the vloume button when a menu pops up giving you the option to reset,factory reset and a couple other options. Scroll down with with the volume keys and press the power button on factory rest. This will take a second and you will get to another menu that says no for the first couple and then yes factory reset. Scroll down to yes and press the power button again. Then you'll be back to the first one and you press the reset option. I know some androids have a different combination of keys to get to that menu. It might be different for yours but it's always a combination or power and volume sometime with the home button of there is a physical button and...
I'm not 100% sure on that I do know the CHU 10xx and the CHU 11xx are not interchangable so I would think those to are either. I would take yours out and look at it then try to find a diagram of the other. I'm guessing Sony did this on purpose. Either to upgrade or make it harder for me and you to repair.