You did a soft reset on the video. Have you done a hard reset? Hold both the top power button and the home button at the same time until the Apple logo appears, then release. If that doesn't work, then try Reset All Settings. Go to Settings>General>Reset> Tap on Reset All Settings. If that doesn't work, you will need to restore the phone to factory settings. Be sure the phone is backed up first. It's possible there's a hardware problem. In that case, you would need to take it to Apple or a reputable repair shop. Or use a 3rd party camera. I do that anyway. Do 3rd party camera apps work?
Sent from from my ancient but trustworthy iPhone 5