If you're lucky, maybe your alarm is like the one on my '97 Subaru. I have a little "secret" button on the left side underneath the dash that overrides the alarm. When my alarms screws up (and it does), I can insert my key, push the override button and crank my car. My button is all the way on the kickboard and is about the size of a pencil eraser. It's hard to find and I've used it a dozen times.
Another thing you can try is to search for a repair manual for your Jetta (I'm assuming that you have a factory alarm). One of the repair books may have install instructions and maybe you can use them to uninstall your alarm (I plan to attempt this with my Subaru since my alarm is going off when it gets cold - I finally ripped the siren out to stop that racket).
There are some links in the Online Repair Manuals Guide.
A stereo shop that does alarms may be able to fix it cheaper than the VW dealer, especially if your alarm isn't factory. And you may be able to get an installer to visit your house to avoid a tow.