Which version of Skype are you using?
Which exact model of ASUS laptop are you using?
Does your camera work in Windows 8 Camera app?
Can you please provide logs as described in this link http://dev.skype.com/support/logging and send them to kmudrovcic at hotmail.com?
You can try downloading and installing Skype for Desktop and see if it solves your issue.
Thank you in advance