Test to make sure that it is the home button that is the problem and not the docking connector assembly.
To do this, open up the (turned off) phone without disconnecting the three ribbon cables. Turn on the phone. Short the two contact pads on the top of the docking connector to simulate operating the home button.
If the simulated home button works, look at the connecting feet between the screen assembly and the docking assembly. If it doesn't, look into replacing the docking assembly.
Reading your description, I would guess that the docking assembly has been damaged.