The Canon EF 20-35mm is a highly rated wide-angle lens that suffers from a common AF malfunction. Many users find the focus control stops working in both auto and manual mode. An excellent article by Piers Hendrie illustrates very clearly how to take apart the lens, and one possible fix for the issue.
The cause of this problem is that the USM ring motor (#4 below) is not applying enough pressure to the focus ring (5). Pressure is applied to the focus ring via a spacer (1), wave washer (2), and a felt ring(3). When you have this issue you can still hear the USM motor moving, but the focus ring does not move.