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There are relays that go bad inside the door window module. That's what you hear clicking. The relays can be replaced or you can purchase a whole new module.
Here is what the module looks like and it is located in the door itself.
One of my friends had the exact same problem and it fixed itself 2-3 days later when the temperature went up. He thinks that the windows were jammed because of the weather...too cold. He would also hear a click. I've never heard of it though on any car, no matter how cold it gets. His driver's side lock wouldn't work either but then started too.
This has happened to me off and on since I bought the car in 1999. I haven't replaced anything. I think it happens due to lack of use at least in my case. I was able to get them working again by removing the door panels and the speakers. Then tap lightly on the end of the window motor while holding down the switch. It should start working again. To prevent it from happening again, I exercise them as I back out of my garage. Then when I park it in the garage, I leave them down about 1/2 inch. Haven't had any problems since. Hope this helps.