My old ASUS G51J webcam worked just fine with guvcview. So its not something that happens to all ASUS laptops.
Other simple ways to test your webcam would be ffplay (i.e. ffplay /dev/video0) and less simply gstreamer:
gst-launch-1.0 v4l2src device=/dev/video0 ! videoconvert ! xvimagesink
Both of these (command line) applications can record to a webm file with some extra work.
Shotcut is a GUI program that I use for recording and editing - give that a try too.