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
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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.
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