There is a pick-up coil that encircles the ignition switch to be the antena loop to communicate with the chip in the key housing. If the loop is shorted or open, the imobilizer will activate. You may want to check the wiring. Its pretty fragile and the first place I'd look.
2004 Jetta GLS TDI 5M Plat. Grey w/ Leather. RC Stage 2, G60/VR-6 clutch, steel skid plate, TDIHeater, CAT 2um fuel flter, Phat Noise, and VDO boost & volt guages.