I have a 2004 Chrysler Crossfire. I had the same problem (except, while driving). I replaced the SIREN (the part cost $200 and I did the labor myself...pretty easy job I must add). The siren is located in the bottom center area of the windshield under the hood. You will have to open your hood. You will need to take off the cowl-grille to access the siren. It's an easy job, but you will need some special tools - like torx bits to remove the grill. Keep in mind that you will also have to remove the wiper blades AND wiper ARMS to be able to remove the rubber cowl -grille. I suggest buying a specialized tool designed to pull the wiper blades/arms from a local auto store. For me, I noticed a problem when my alarm would go off for no apparent reason when parked, and my external lights were blinking too. The alarm sound also sounded very weak and intermittent when it did happen. As soon as I installed the new SIREN everything was fixed. I also noticed that my new siren now makes a cool beep sound when arming and disarming the siren (alarm). Hope that helps.
Where did you order it from if I may ask