Re: home button is broken
If your home button is damaged, you can request a repair through Apple (as they still cover maintenance on the 4S) or 3rd party...you can even try replacing it yourself (I don't think the home button is too terribly hard to replace). You could also tweak your accessibility options to assign another button to get you back to the home screen, but that is simply a temporary fix.
As far as your password...you're out of luck there. You could always restore the device and setup as new, but you'd have to add everything back to it afterwards (which would be quite difficult if you didn't have a properly functioning home button).