After the original (flawed) update to OS X 10.8.5 was installed, the internal camera of a 2013 MacBook Air would not work in Skype and some other third-party applications. The flaw was fixed in a supplemental update. However, if you followed some questionable advice that was circulating on this site to hack your system before installing the supplemental update, then it will not restore camera functionality; in fact, the camera won't work at all. The solution in that case, most likely, is to install the 10.8.5 Combo update.
In the future, I suggest you ignore advice to hack your system by replacing, removing, or changing built-in system components.