(0) Your problem might be a bad Skype install.
Reinstall the latest Skype version that is compatible with your Mac OS.
If the problem persists, consider the following:
(1) When you tried Apple's suggestions, IF, in EVERY user account you tested, the Apple apps also exhibited the problem (i.e., start an Apple app session, quit that app, and try an Apple app again BEFORE you launch Skype,) your Mac OS software may be damaged.
Properly applying the latest COMBO update for your Mac OS can sometimes correct software problems. Here is how I do it:
• Use your Mac's Disk Utility to repair permissions and then
download and apply the latest Combo Update, for your Mac OS,
the current one is at: http://support.apple.com/kb/DL1400
• Repair permissions again immediately following the system restart
that completes the Combo update.
If the COMBO update did not resolve your problem, reinstall Mac OS X. Then apply the Combo Update again before testing your iSight's operation.
If your problem continues after proper reinstall, make a current backup, and then use the final "Troubleshooting" suggestion:
"... contact Apple or an Apple-Authorized Service Provider for service."
(2) When you tried Apple's suggestions, IF, in EVERY user account you tested, your problem ONLY occurs after you have launched Skype, Skype's comprehensive support system should best be able to help you use their product with your system.
Start here: https://support.skype.com/
You can also search or post for help with your problem in Skype's dedicated Skype Discussions for Mac. The Skype users who post there may have already solved the same problem.
If no other Skype help works, you can sign in and ask for email help directly from Skype's Technical Support people.
Mac OSX 10.8.2