If the external camera works on another computer but still doesn't work on yours, you should check if the USB ports aren't faulty or covered with debris.
If you have another computer, you can use it on that device and check if the camera works. Then you need to confirm if the external camera is indeed functional. You could also unplug the camera and plug it back in. If you are using an external USB camera, fixing the Skype camera issue is as easy as making sure that the camera is plugged in correctly.
