I don't have any experience with this particular laptop but the first thing I do when I have strange issues with laptops is 1 remove all power after shutdown including power brick and battery if possible. Let it sit for a while then try and start it up.
The second think I do is make sure the firmware is up to date. there should be a utility from Asus that will do this so take a look a their support site and see what they have for this.