Never worked? What a dud, I would have called up the dealership and *****ed at them for it (I've gone back on warranty for a whole door panel because three inches of vinyl warped and a cruise control switch because the LED went out.). Anyway, I think you could replace it with one of those LED theft deterrant blinkers made by Varad possibly. I replaced mine with it and they come in any color you want. Plus they're much more visible than stock so people know your alarm's on.
If there is no electricity going to the LED after testing, I have no idea. Check the fuse, but I wonder if your alarm really works (?).