I actually had the same problem and while frustrated with the phone

in the car, I dropped it about onto the middle armrest section of the car from about 4 inches above it and *magically* the dark screen went away.
Now I don't know what my involuntary "scientific" approach to fixing it did, but it worked!
Just don't drop it on concrete from 5 feet above! I did it...(not on purpose of course) and it cracked my screen...
Results may vary...
