2003 BMW 530i Key FOB not working

Hello, The vehicle has a limit to how many keys can be synced to it at once. Also, since the key is working for the doors, it is still synced to the vehicle. Since the key has been learned by the vehicle and functions in other capacities, I immediately blame the vehicle. You will likely need a professional grade scanner to determine where communication is broken, but I would be most concerned about the electronic driveaway protection control unit (EWS) or the ignition switch. I would be slightly concerned about the general module because individual circuits can fail within the module. In either case, it will come up during diagnostic testing.