Alarm System bypass

That absolutely can not be done. If it was possible, what would be the point of having it?

I run into this with my 1993 Dynasty too. I put a battery in it about once every other year to drive it, and it always goes into anti-theft mode but without blowing the horn. The procedure to turn the system off is to use the key to lock and unlock a front door, like you normally would do. If that doesn't work from either door, suspect there are broken wires between the door hinges. There's multiple wires in that harness for the disarm switch.

Look under the hood for a round black switch along the edge of the inner fender, right under where the edge of the hood meets it. If an alarm switch is used, it is usually on the driver's side. Unplug that switch. If that solves the problem, I'll describe how to readjust it.

Next would be to connect a scanner to see if the disarm signals are being received. In most models there is a linkage between the lock cylinder in the door and the disarm switch that can pop off, then the switch won't do anything. Less common would be a defective switch, but you would still be able to disarm it from the other door. The scanner will also show the reason the alarm activated.