Firstly is the alarm a factory or aftermarket fit?
With a professionally installed Cat 1 alarm the system operates in normal mode from the vehicle battery, but the system will normally have a back up powersource concealed somewhere within the dashboard, engine bay or occassionally within the siren unit if fitted. The idea being that if the car is locked and the alarm is set, it cannot be disarmed by disconnecting the vehicle battery. Essentially the system monitors the current drawn from the vehicle battery which is a closed switch. If the current drops, which from a 12v source on a vehicle is quite high, the alarm will sound using the back up power source (normally a 9volt battery).
If you are trying silence the alarm by disconnecting then this may be why the symptoms are there. If the vehicle is unlocked and the alarm is not set, then you may have an electrical problem with the alarm in that when not set, the system is still monitoring the operating current.
Unless you are an electronics expert I'd say a main dealer could sort it...at the cost of the whole alarm system no doubt. Probably cheaper and better to take it to a professional alarm installation company. They would be able to fault find and fix the system rather than just replacing the whole lot.