The Home button not working can be the result of dropping your phone, getting your phone wet or just dust (or sometimes stuff just tanks). Fortunately it’s a hardware problem with a software workaround.
This will work with an iPhone, iPod Touch or iPad using iOS6 or earlier.
1. Hold the power button down to force a full shutdown and restart of your phone.
2. Touch Settings
3. Then General
4. Scroll down and find Accessibility
5. Under the heading “Physical & Motor” turn on AssistiveTouch.
6. You’ll notice a little glowing circle in the top left of the screen.
7. Touch the circle and there’s your new Home button!
I hope this works for you, if not you might find a few other suggestions on this Apple.com thread.