One BIG point to bear in mind is that the alarm/siren is separate from the immolbiliser. The latter uses the RFID in the key, f you can start the car with the alarm/siren blaring away, then the issue that you are having with the alarm/siren is a separate issue, and most likely it is the battery in the alarm/siren that is on its way out.
To check this, when you connect the main car battery and the alarm/siren starts blaring, get into the car and start the engine. If the engine starts, best thing to do is get out of the car and wait. You have to wait for the alarm/siren to stop blaring (it will stop), and then wait a further 30 minutes. Then see if you can lock and unlock the car several times using the buttons on the keyfob. If you can do this, then finally unlock the car with the button on the keyfob and get in, and you should find that the alarm/siren is behaving itself.
But if the alarm/siren goes off again when you get into the car after having waitied for 30 minutes, then IMO the battery in the alarm is dying and needs replacing.