Are you using the original touchscreen or did you get a whole new digitizer with that home button?
If it's the original touchscreen then you may have torn the ribbon cable a bit when removing it or didn't put it all the way into the slot.
If it's a new touchscreen that isn't an official apple touchscreen then you may have gotten a defective touchscreen or, as some have found, your ipod doesn't like that particular touchscreen. Many people have gone through a few digitizers before they found one that worked with their ipod.