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1996 is a DAS2 vehicle, there were no transponders in this DAS system, that didn't happen until 1997 with DAS2a. Thats when you had the antenna "collar" around the ignition cylinder and a transponder in the key. I am relatively sure that key (remote part) will work "out of the box" or you might have to synchronize the key to the car, which would be explained in the owners manual how to do. (easy diy job)
My thought on the antenna going up is tha it might be the ignition switch itself (electrical part) as these are a fairly well known problem.
The problem with the car not recognizing that the key is removed could be a cable adjustment or like you said, the ignition lock. IIRC if the key is removed the shifter should lock (should say one way or the other in the owners manual), if this is true try pulling the key and see if the shifter will move, this is I believe all inter-related by a cable from the shifter to the ignition lock, could be a simple adjustment.
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