Do i need a new siren now ? or is it just the 2 x3.7v batteries in the siren that need replacing ?
You can not tell without sawing the module apart, but I can say from your symptoms that there is a 90% chance that your batteries DID go bad, and also leaked all over the circuit board.
Probably time for a new module, make sure you get the updated one that beeps on lock/unlock.