These past few days, the iPhone I use had a black screen. For all purposes, it looked like it's dead, or switched off. But the alarm, which is set to go off at 6 everyday, made it ring and vibrate like crazy every morning and I couldn't turn it off. Calls were still going in, but I could see nothing. I could still use the cable to charge it and to sync it with the laptop and I'd hear the "clink" noise coming. So it wasn't dead, but neither was it functional.
They say Google's your best friend, and today it proved to be. A quick search on "iphone black screen" returns this page: http://seogadget.co.uk/iphone-display-blank-screen/. (The author had written, in his following post, that some site leeched off his post—I'm not going to do the same thing.. hence the link). But it basically says that you should hold down the "Home" round button at the bottom and the "Wake/Sleep" button on top, and the phone should reboot itself nicely.
It worked for me. Hope it saves someone the anguish, or having to find a pile of clothes or blanket in which to hide the vibrating iPhone. Read the comments in the link to amuse yourself :)