The click you hear when you press down, is the auto-down relay. Mine was doing the same thing.
Be careful taking the plastic apart because there are a few screws holding it in as well as those stupid plastic clips. The panel can be taken off without removing your speakers by the rear view mirror (if equipped).
Do not remove the motor from the assembly while it's in the car. You will hurt yourself. It is spring loaded and sharp. The entire assembly will come out in a matter of minutes. If I remember correctly I had to bend a tab on the left side of the track out of the way, and remove a bolt or two.
You will need two people though. One to hold the window up to the correct height to get the motor components out.