The 5C's rear housing design is plastic as we known. This means it flexes when dropped or bumped. This causes the screen's "tabs" at the top to loosen thus breaking ribbons or destroying the circuits (ESD, Liquid, etc). The plugs controlling all of these functions lye at the top right corner of the back of the screen.
If the top of the screen is protruding then take it straight to Apple for a replacement. If the glass cracks they won't cover it. If the don't we can always help or you can learn and buy parts right here on iFixit.
If you happened to open it up and the screen isn't connected the other half then the ribbons are broken. You'll need a new screen and front camera to fix the issue.