I had the same problem with the home button acting crazy. The problem is on the new screen there are metal contacts that are exposed and they are touching the metal frame making it seem the button is being pressed. If you look on the old screen you'll see strips of tape covering these metal contacts. You can either peel them off and put them on the new screen or just use some electrical tape.
Be very careful when you detach the touchpad ribbon. You could disconnect the other end that is inside the touchpad. In fact I would recommend you use a plastic spudger to release the clips on the sides of the battery holder, and then lift the latch to the ZIF socket of the touchpad. If your touchpad is not working upon reassembly, then the other end of the ribbon cable my have came loose in the touchpad. Use a plastic opening tool to remove the back of the touchpad, and lift the brown latch of the ZIF socket and reinsert.