Volkswagen key fob won't work.

The key fob for my 2006 Jetta suddenly stopped
working. The battery shouldn't be an issue because
the red light on the fob still blinks when I press a
button. I tried replacing it anyway, and nothing
happened. I tried reprogramming it based on what
the manual said and what I could find on YouTube,
but nothing worked. One odd thing is happening,
though. I can hear a faint click coming from the car
when I press any of the buttons on the fob, so my
car is at least responding to some kind of signal.
Plus, my other fob works fine (despite being in
rough shape), so the locking mechanism in the car
isn't the problem. I'm at a loss.