When you drop your phone it can brake things in the inside because of the impact. In the country that i live in apple technicians aren't allowed to replace screens because of this reason. Open up your phone and see if there is any damage you can notice compare it with an image from google or this website showing the inside of an iPhone 5c.
Is the phone jailbroken. Does it pop up on itunes when plugged in? If it pops up on itunes do a hard reset. hold the sleep and home down together until you see the "Plug into itunes" icon. Hope this helps. :)