OK, you changed the display and installed the original home button and Touch ID doesn’t work: then this helped me:
first check that all home button connectors (right at the button and where it connects to the mainboard) are clean, set up properly and have a good connection.
If the problem still exists:
grab your old display and take off the metal shield from the back. 6 or 7 little screws, not too complicated. Take note which screws in which order you replaced to get it off. It has a home button ribbon cable glued to the inside of the shield.
Open your phone one more time, take the display off, exchange the metal plate with the glued-on cable from your original broken display, assemble everything back together: and there you go, good change Touch ID it will work again.
Just be very careful when assembling and disassembling, to not bend the cable too much or stretch it etc, use a good fixation as described in the tutorials.