One of the inputs that the security system needs is the input from the lock cylinder switch (door locked / unlocked indication). The lock cylinder switch is not on the actual lock cylinder, it is in the door latch assembly. As such, shaving the lock cylinder still leaves you with the cylinder switch in the latch assembly. I had my latches out of the door this spring when I was replacing the rear window sash; but, I did not pay particular attention to how the lock cylinder switch is operated. I think it is operated directly by the lock motor and as such removing the actuating rod from the lock cylinder to the latch should not prevent operation of the lock cylinder switch. But, I don't know that for sure.
You need to get a .pdf copy of the 1991 service manual via the links in the Prime Wiki. Look in the electrical section for the door lock mechanism and you will find the test procedure for the door latch including the pin out diagram for the connecting plugs. You can use that information and a multimeter to confirm that the lock cylinder switch is operating when you operate the lock knob. If you were previously getting false alarms the lock cylinder switch or the lock switch contacts may be getting dirty / wearing and finally died. This will prevent the security system from arming. It is also possible that when the actuating rod from the lock cylinder was removed it buggered up the operation of the lock cylinder switch. Only testing will confirm whether you have a problem with the switches in the latch. If the operation of the two switches in the latch checks out fine then you have a problem someplace else in the security system and you need to go through the input check as described in the service manual.