Can of WD-40
Take the WD-40 and spray just a little amount of it on the home button.
Gently rub the WD- 40 that you just sprayed, then press the home button repeadly until the button gets unstuck and you should feel the button start to click again.
Wipe off the access of WD-40 on the device. You might have to repeat the process one more time, which only depends on how bad it's stuck.
I have used this process on more then 10 devices, and also on different ranges of models as well. I can assure you that this will not damage your device. Please take precautionary measures.