One of these will fix your camera problem:
(1) If restarting your Mac doesn't fix the problem,
(2) use Apple's http://support.apple.com/kb/HT2090.
(BTW - The Troubleshooting article calls the camera an "iSight". However, after the article was published, Apple has changed the built-in camera's name on newer Macs from "iSight" to "FaceTime" and then to "FaceTime HD." Regardless of the name of your built-in camera, the same info and troubleshooting applies.)
Be sure to test more than one Apple app (Photo Booth, FaceTime, iMovie, QuickTime Player, etc.) in more than one user account. Do NOT use the "Guest" account for this test. If you do not have more than one user account for the testing, create a new one now. If you need help, how to do it is explained in http://support.apple.com/en-us/HT201754.
A "Standard" user account is all you need for testing.
(3) If your cam won't work properly even with Apple apps, use OS X Recovery to completely reinstall your Mac OS from the Recovery System stored on your startup drive. Don't bother testing Skype or other third-party apps until you have your camera working with Apple apps.
(4) If none of the above suggestions resolve your trouble, contact Apple or an Apple-Authorized Service Provider to have your Mac professionally serviced. Be sure to backup your Mac and deauthorize iTunes before tendering it for service.
Message was edited by: EZ Jim
Mac OSX 10.11.3