keyless remote problem

I have a 1993 Explorer with the factory alarm installed. The problem is that on the key fob the alarm will not set I can unlock the car but cant set the alarm. I have replaced the batteries. I tried pushing the button inside the car to activate the alarm and I hear a clicking noise but the alarm will not set. I have had this problem in the past where the alarm system needed to be reprogrammed. It usually happens after I turn the key off and the alarm goes off 3 or 4 times locking and unlocking the doors and I have to hit the valet switch and push disarm. This time the alarm will not activate nor lock the doors only unlick. Does anyone know how to reprogram the alarm system. I do not want to pay Ford another penny to reset what I believe to be a faulty system.
Thanks

I am not familiar with the setup for a 93, I have a 97. What happens if you press the lock button 2x on the fob? My car confirms locked and armed with one honk. If it honks 2x it means that it is locked but not armed. Usually happens if a door is not fully latched or the door ajar sensors are stuck or bad.

I was going to suggest changing the batteries, but I see you have done that already.

Try reprogramming the remote:

Turn ignition to RUN or ACC. Momentarily jump pins in programming connector located in LR quarter panel area. All doors will lock then unlock to confirm programming mode. Press any button on 1st transmitter. Door locks will cycle to confirm programming. Press any button on 2nd transmitter (up to 4 transmitters total possible). Turn ignition to OFF. Locks will again cycle to indicate end of programming mode.