We have an 02 Laredo that is missing the key fob for the keyless entry. Randomly, when you unlock the door with the key, the alarm does not de-arm and we have to shut it off by turning on the ignition. Any ideas? Also, can we take a key FOB from another JGC and "reprogram" it to this one and how?

there is a switch on the back of the lock cylinder that could be bad,or falling of the lock.or the wiring in the door jamb could be a problem