So you do not have a screen backlight? But the pixels do fire up and display correctly?
I'd say its something with the digitizer assembly. As Tonefox said, the iPhone is not considered to be user servicable, but maybe they will help you get a diagnosis free of charge.
At that point, it is very possible to fix it yourself. Look through iFixit.com, they have some amazing guides and parts for sale, everything you would need to fix a 4 or 4S.
I dropped my phone off of a golfcart, onto a paved surface at 20 MPH. I replaced my front and back glass panels in about 2-3 hours. Stressful, but I spent $80 instead of $400 for a new phone :-)