The iPod has a liquid crystal display. A very thin capsule with a chemical compound which builds up the picture under an electrical charge. Likely is this capsule ruptured as a result of the fall.
There will no longer be any picture or pattern. All you are seeing is the electroluminescent screen (backlight) which shines through the crystals in the display.
This must be replaced as a complete unit. Relatively easy on the 4th gen nano.
The contents of the display are regarded as toxic so take precautions if you see any of this inside. Mop up carefully with camera lens tissues.
After plugging in the replacement give it a quick try before pushing it all back into place.