Not sure if it helps you to back up data, or do anything else, but try to attach and external monitor too if you're interested.
Since you are likely using Win8, you may want to try to get into the bios (or safe mode?) if you can just to see if it could be software related, but not sure if the bios can be affected by the same problem too.

Don't expect it will help, but try pressing Fn+F6 a few times to brighten the screen and moving the position of the screen to see if it makes any difference.

If nothing seems to work, you may want to contact your local ASUS support to troubleshoot and arrange an RMA if you don't have any better options through your store.
http://www.asus.com/support/callus

Good luck!