Usually, this means your lcd is faulty. You can try opening up the phone and checking the connections for the lcd, but they don't usually come un-done. If you're gonna order the screen yourself, make sure you open the phone up first to make sure it's not the cable and to get used to working on them. Good luck!
Usually when a phone is dropped, it cracks only the glass (pretty much the lens for the lcd). It sounds like it fell hard enough that it made the lcd malfunction. If there is no visible crack on the lcd, it could just be the wiring inside. This is usually not the case though. You'll have to buy the lcd and glass combo online. I think they're cheapest on Amazon.com at around $130, last time I checked. As for the touch still working, there is another part called the digitizer. This is what senses your fingers. It's a lot more flexible and resilient then the lcd and glass. Thankfully, that also extends to impact protection. :) Hope this helps and good luck!