Your'e correct, it is a 2004 and it's the same with both keys. But, the radio wouldn't pick up any statioins and they installed a plug in amplifier, which may have been aftermarket.
I was not talking about the radio antenna but the antenna and the amplifier receiving the radio signal from the remote key. But good that you mentioned this because these may well be connected. I did not check how your car is built but likely the remote RF receiver antenna amplifier is combined with the FM/AM radio antenna amplifier.
You did not comment my previous question about the RF versus IR test. Say if you stay close to the car but look away from the car, pointing your key away from the car or if you stay close to the car door that has the IR window (and receiver) and carefully point your IR key towards the door receiver, do you notice any difference? I'm after testing the IR receiver against the RF receiver for the remote key (it operates via both).
If you are further away from the car, say 30 to 100 yards, can you open and close the doors at all?
If you operate windows with summer convenience function, do they work at all, do they work intermittently or perfectly? This is a test for the IR part alone, windows won't open or close via the RF signal.
If it is intermittent in all cases, it becomes a bit difficult to guess which part is bad.