Let’s call your original phone “Phone A” and the for-parts model “Phone B”.
You say you moved Home Button A onto Display B, and Home Button A didn’t work.
If you put Home Button A back on to Display A, does it work on Phone A? If so, then either Display B is bad or Home Button A wasn’t seated properly on Display B. If not, then Home Button A was damaged during your repair attempt. The Touch ID circuitry is RIDICULOUSLY delicate and very easily damaged.