From my experience the home button won't work if it's not low enoughh to make contact with the contact areas it is supposed to sit on. When you replaced the screen , if there was too much tape put on, the button won't sit low enough to make contact, or if there was not enough tape the screen may not sit close enough to make contact again because when I replaced mine, I didn't have enough tape to hold it tight against the chassis. If it worked before you changed the screen I doubt it went bad just by removing it. Either way you will probably have to take it apart again. Since you have to take it apart again, you could remove the screen, remove the button from the screen and just put the button on the area on the iPad where it should sit and see if you can get a response out of it. It's possible the screen isn't exactly in the same place it was put at the factory when you took it off and put in back on. Since there are no wires to connect to the button it has to sit exactly on the contact points in order to work...hope that makes sense..And I hope that helps..
Let us know what you find out..