Had a similar thing when I got my car... it turned out the Alarm Siren was dead, but better than that, it had been switched OFF in VCDS
The Siren is riveted on and can be got at through the offside wheel arch, I didn't bother having a go at it, as I thought it'd been through enough, lol, but it's an easy enough job once you've drilled it out, can grab them on eBay for ~£30.