It does sound like your backlight, since you can see the icons. First I would go through the usual reset routine, just in case and it can't hurt.Reset the iPhone by holding the sleep/wake button at the top right of the device and the home button at the bottom center of the face at the same time. Hold them both until you see the screen go black and the white Apple logo appear. When this happens, you can let go - the iPhone is rebooting.
Resetting the iPhone should not remove or delete any data or settings. If that does not help, I would disassemble the phone and take a closer look for any visual damage aswell as check closely to make sure that all connectors are seated and all cables are in good working order. Do make sure that you check all connectors for corrosion very closely and clean off any corrosion. Isopropyl alcohol and a soft brush will work for Also check for corrosion in the area of the coil.
I suppose it is possible that the backlight coil got knocked out. I would go for the cheapest part first, so a new LCD might be the first step and after that you may be looking at a new logic board if you can not isolated the error any further. Here is a little bit more information http://forums.macrumors.com/showthread.p... But those are just my 2 cents and I could most certainly be wrong.....let us know how it is going. Good luck.