First thing to try is to reset your device. Press and hold the Home and Sleep buttons simultaneously ignoring the red slider should one appear until the Apple logo appears. Let go of the buttons and let the device restart. See if that fixes your problem.
Is this how you restarted?
Could you have a dead battery? Plug your phone into the wall charger that came with the phone and leave it plugged in overnight. Then try to turn it on.
If it still doesn't come back to life make an appointment at an Apple store to have theHome looked at.