I have a similar Asus laptop and spent a month trying to get the webcam working in skype. Ended up just buying a logitech webcam for $25 and it worked no questions asked. I know this is not the answer you are looking for, but I have been down this road and it is fraught with peril.
good luck
Did you check to see if the drivers are installed or try updating the driver for the webcam?
Control Panel>System & Security>System>Device Manager>Imaging Devices
It should show the webcam there, if not then the driver needs to be installed or updated.