We have a 2003 Jetta that sometimes sticks in Park. Cold weather aggrivates it and warming it up eventually releases it. The dealer acts clueless, but we suspect someone must have solved this already.
there is a TSB on this year, but it lists “trouble getting out of R”, not park.
maybe you should call VW, and ask them about this TSB.
Could be the neutral-safety switch. This will prevent you from shifting out of park unless you have the brake pedal depressed. Check the switch on the brake pedal, it could be out of adjustment, or the solenoid in the shifter could be going bad.