Last question first: sounds like the key is not in sync with the car, on the Immobilizer. I don't remember the procedure, and it might be different for a '99, but the manual should have it. Something like putting the key in the ignition, turning to run, pushing the button, etc.
As for the first question, if the remote works at all, I'd tend to think it was working fully. Not to insult your intelligence, but just how fast are you pushing it? I'm not sure how I do it in mine, but more often than not I have to do it twice, as the first time I just don't get the second click quite right.
Did it ever work? Never worked? Maybe it's something for the dealer to check out--there have been stranger electrical gremlins out there, and perhaps your's just has one of the weird ones.