Alarm system stays on

This sounds like you have a shorted door lock solenoid or the alarm module is going out (BCM). I would try unplugging all of the lock actuators to see if you can get the alarm to stop and then plug them in one at a time to find the bad one. If that does not seem to work I would get a used BCM and try plugging that in. It will need to be programmed for the car.

Here are some wiring diagrams and the location of the BCM which is the alarm:

Please let us know what happens.

Cheers, Ken