Look at this picture of the home button controller:
[image|120140|size=thumbnail]
That is the part that is responsible for that clicking action. That part is probably out of place, missing or broken. I would take the panel off (sorry, I know it's not easy) and see if you can see the home button controller. Check and see if the whole assembly is intact and if it's in the right spot. I'd also try to depress the button as well and see if you can't get that clicking action to work.
Repair Guide:
[guide|3615]