Sorry to hear about your touch ID on your iPhone.
A couple of questions to help you.
1.Do you transfer the backplate with fingerprint extension cable from the old LCD assembly to the new LCD assembly?
If you did, there is a good chance that the backplate with fingerprint extension cable is bad is often the case with ones that are not the original apple fingerprint extension cable.
2. There is a good chance there is a tear in the fingerprint extension cable or that one of the connections is bent. You can post a picture of both the female and male connectors to the home button and fingerprint flex cable and I can take a quick look. If the fingerprint extension cable is broken you can buy one from ifixit.
3. Worst case scenario is that you have a small tear on your home button flex cable and you will never be able to have your fingerprint work again unless you can get apple to replace the screen for you which most likely they won't. You can purchase a new home button from ifixit or maybe your local repair shop and the home button will work again but the fingerprint scanner will not.
I hope this helps!