Shutter clicks - no image results - 60D

New to the Canon 60d. Taking movies has not been difficult. But I also need to use it as a still camera. In Live View, I click the shutter button, and the camera does not take a picture unless I keep the button depressed for way beyond the "decisive moment." The camera makes a sound as soon as I press the shutter button, and I've gotten fooled that I had taken a picture when I hadn't. My only answer so far is to avoid Live View.

When I try to use Live View with the self-timer set to 10 seconds, no image is taken at all.

Thanks for any advice.

Bob C