Ok, mine scared the sh*t out of me also. Mine was fully charged, still plugged into the charger and not being used. Suddenly say only a * astrick in the center of the screen. Wouldn't turn on or off, even when I plugged it into the computer.
Read the above about doing a hard boot. That worked, but now I'm worried. What caused it and will it happen again? This is my 3rd iPhone (3gs, 4, and now this 4s). Never had this happen before.
Just got off the phone with Tech Support. They indicated it's not uncommon, BUT if it continues, may have to go to the store for a replacement.
Now THAT doesn't give me a lot of faith in this phone! At least now there is a record of it malfunctioning, and I will stay on top of this.