From what I've learned recently, you have two options. A bypass that sort of generically gets around the security. I believe it's programmed from your key. The other type, is the one that requires a key. I'm totally guessing, but maybe the problem is that it's a programmed type and the car doesn't like it. Maybe a new bypass with a spare key is what you need.

I also have a 2004 GT (maybe a GT2?). Take it with a grain of salt, this info came from BestBuy.