[P-51 Mustang]

I have a 1998 Boxster that I only have one key too. The key I have doesnt have the fob on it it looks like a vallet key or because it doesnt have a chip in it or anything. When I go to lock the car with the key from the driver door it everything locks fine but when I try to unlock the car with the key from the door it wont unlock. I have to go to the passenger door and unlock it and only that door will unlock then I have to go inside and put the key in and press the unlock on the dash. All the doors and trunks lock and unlock fine from the button on the dash. What could be causing this? If I got a new key from the dealer that has the keyless remote on it would that work to lock and unlock my car? How can I tell if the sensor that recieves the signal from the key (I am assuming it is that piece in the middle of the dash by the windshield) works??? Thanks for any help!!!