It's possible that the software crashed and needs to be rebooted. Press and hold Home and Power button until you see the Apple logo. When it appears, let to of both. Your iPhone will power up on it's own.
Sometimes rebooting alone doesn't work. In that case, toggle the Mute switch a few times, then reboot again.
If possible, use a different charging cable and charger, as well as a different power outlet, just in case your iPhone was not charging.
If nothing happens, take your iPhone to the next Apple Retail store for diagnosis.