I'm guessing (after having two cars, not Subaru with the same thing) that the bullet looking thing is part of the immobilizer. Usually you have to put the end of it against the socket in the dash before you can start? If it still starts without you having to do that it may of been bypassed. Or perhaps its more of a, the thing has to be in a certain radius of the car to start without having to actually put it against the socket.
Have you tried to change the battery? Just because it has enough power to flash a little red light, might not have enough to send a signal to unlock/lock the doors?
Someone else will probably come along soon and tell me I'm wrong