First off, take a flash light, and shine it on the display to see if the LCD under the glass is cracked. If the LCD is damaged, you'll need to replace the display. If the LCD isn't cracked, take a look at this guide (Galaxy S III Display) and check the display connections at the motherboard first to make sure the display connector didn't become dislodged from the drop. If unplugging and replugging the display cable doesn't fix your problem, you might want to consider a display replacement. The replacement procedure is relatively straight forward for these phones (I've replaced roughly 10 displays on various S IIIs over the years). But be careful with the Wi-Fi antenna connections, I damaged one of them from prying on the first S III I repaired! Good luck!