It wasn't dropped, it has battery power... It just went black and has no power. I've taken the sim card out and put it back. I've plugged it in... nothing!
I've seen this once. Try rebooting the device by holding down the lock button and the home button until an Apple logo appears.
If that fails then you could try plugging the phone into iTunes and resetting it. If neither of my suggestions work then it's probably worth taking the phone to the Genius Bar.