Hey, I wouldn’t recomend buying from amazon, eBay offers more premium screens. Since the home button worked on an old screen, it’s probably a faulty screen. Always buy OEM Apple displays. They will never have flaws
There are 2 possible problems… 1- the connector to the screen and the home button isn’t connected correctly… this generally happens when the aftermarket Home button connector isn’t perfectly in the right position, thus leading to a crooked connection 2- the actual home button receiver (female connector) connector from the screen is broken… is the replacement screen an aftermarket or a genuine OEM Apple display?