A broken home button on the iphone makes the phone unusable since you cannot get back to the home screen from a launched app.
The solution is however rather simple.
-hold the powerbutton and slide to shut down the phone.-Turn it back on with the powerbutton-Once in, go to settings, general and turn on passcode, enter a code you remember well-click the power button once to close and once again to open
-your screen will look different since you have to enter the passcode-rather than entering the code first click emergency call and once there press the back button on the screen
-enter the passcode and you will then get to the home screen
Basically with pass code turned on you will be able to get back to the home screen by making a quick visit to the emergency call screen before entering the passcode.
As far as I know there is no way to quick jump between open apps which requires double click on the home button :/
For me this means that I can survive until I find a good deal on a new phone or even wait until september when the new iphone expects to be released.