Sounds like you will need to replace the screen.
Its not something that can be fixed thru software or anything like that.
Either bring it to a repair shop to replace the screen or bring it to Apple if you're still under Applecare warranty.
Explain?
You either dropped it or the screen died that's all. What is there to explain? Electronics do mulfunction, break, burn out etc...
Its a hardware issue whether you want to believe it or not.
You CANNOT fix it by pressing any buttons or restoring it thru itunes.
If you have Applecare warranty bring it to Apple so they can replace it, if not find an iphone repair place to fix it or buy the parts and try to repair it yourself.
Not much else you can do.
The screen itself (glass) per se is not broken. However its ability to display is not functioning as it should.
This exact same problem occurred to my son's 3GS. Luckily we had applecare and they tried to change out the screen, but that did not fix it, so they replaced the whole unit. The problem was with the logic board.
However, I would suggest you at least try some of the "fixes" out on the internet. One might fix it for you.