Sorry if this is a duplicate response. I don't see the response I made earlier.
On my 2001 the steering lock is mechanically actuated by the bar connecting the key cylinder to the electrical connector on the left side of the steering column and I'm assuming you have the same basic setup. If the mechanism to move the steering lock is broken, the steering wheel won't unlock. If the car is powering up, the bar between the key and the electrical connector is working so the problem is most likely with the lock itself and will require that the housing be replaced. It's an aluminum casting that has the electrical switch on the left, the lock pin in the middle and the key cylinder on the right. It bolts to the bottom of the steering column.
VW changed the design several times so make sure you get the right one for your car.