Unable to activate touch ID on this iphone

Unable to activate touch ID on this issue happened afterchanging the broken screen and the battery.

Try this: Go to Settings → General → Reset → Reset All Settings. ( if you’ve enabled restrictions passcode then you’ll be asked).

This will reset all settings. No data or media will be deleted. Next, try to set up Touch ID. Hope this would be work in your case.

Open on the Touch ID menu and make on the "iPhone unlock". After click on add fingerprint.

First, what model is it? And, has this phone been serviced?

Try to backup and Restore process and then check it out.🙂

Has this problem only starting showing after a screen replacement?

It has for me. Cracked my screen last week and had it replaced asap - now touch id doesn't work no matter what i try

Replacing the screen and button will disable Touch ID, unless you have Apple make the repair. If Apple did it, you have their parts and repair warranty, otherwise you're out of luck.