I can hear it click when I lock or unlock the car. Lights still flash and car still unlocks/locks. Is it possible for just the siren to go out? It is an older Viper alarm, If I remember correctly it is a 600 ESP model.

yes its possible. especially if its in a place that gets wet. you could also check the wire leaving the siren to make sure it didnt break somewhere but you probly just need a new siren.

Did you check for a blown fuse, for the siren?