Thanks to Wingnut and everyone else who added information regarding that bobcat-being-neutered sound that we hear just after the engine is cranked over. I just dealt with that sound coming from my 2002 Jetta TDi on Saturday, and I thought it would be good to throw in my two cents worth regarding the steps involved.
I found that, on my 2002 Jetta TDi, I did not need to access any parts from underneath the car. Everything is accessible from under the hood. Here is the procedure that I used:
1) Anyone with a Monsoon radio, as I have in my car, jot down the frequencies of the stations that you have programmed on the "FM" band. The "FM1," "FM2," and "AM" bands are not affected by disconnecting the battery. Neither are any other vehicle functions other than the trip odometer and clock.
2) Remove the battery cover (lifts off).
3) Disconnect the heavy red wire from the positive battery clamp using a 10mm socket wrench, open-end wrench or box wrench.
4) Disconnect the positive battery cable from the battery using a 10mm socket wrench, open-end wrench or box wrench.
5) Disconnect the negative battery cable from the battery using a 10mm socket wrench, open-end wrench or box wrench.
6) Unclip the plastic wire housing piece from the battery box by releasing the clips on the left and right sides of the box.
7) Remove the two screws that attach the left headlight rear cover using a #2 Phillips screwdriver. Remove the cover.
8) Loosen and remove the battery hold-down bolt located at the lower front of the battery using a 13mm socket attached to a socket wrench with one twelve-inch extension or two six-inch extensions. Remove the hold-down clamp also. Remove the battery from the vehicle.
9) Loosen and remove the four bolts attaching the battery box to the engine compartment using a 10mm socket, extension of your choice and socket wrench. Remove the battery box from the vehicle. (Two plastic wire housing pieces will detach easily during this step--note how they attach to make reassembly easier.)
10) Remove the nut holding the wire bundle tray to the upper starter mounting bolt/stud using a 13mm socket, a six-inch extension and a flex-head ratchet wrench. Slide the tray off the bolt/stud.
11) Remove the nut holding the air conditioning tube bracket from the lower starter mounting bolt/stud using the 13mm socket, six-inch extension and flex-head ratchet wrench. Slide the bracket off the bolt/stud.
12) Remove the small wire from the starter solenoid by squeezing the retaining wires on the connector and sliding the connector off.
13) Remove the lower starter bolt/stud using an 18mm deep socket, a six-inch extension and a flex-head ratchet wrench.
14) While supporting the starter with one hand, remove the upper starter bolt/stud using an 18mm deep socket, a six-inch extension and a flex-head ratchet wrench. Carefully lift the starter out of the car.
15) Clamp the starter in a vice (if available) by one of the mounting ears.
16) Remove the 13mm nut and washer that attaches the wimpy braided copper wire to the solenoid and slip the wimpy braided copper wire off the solenoid stud.
17) Remove the two long screws from the non-business end of the starter using a 7mm socket, open-end wrench or box wrench. Carefully separate the starter motor body from the gear/solenoid housing.
18) Remove the three screws holding the solenoid to the housing using a T25 six-lobe driver. (Be very careful as the screws are seated firmly and can strip out easily.) Slide the solenoid body off the solenoid piston.
19) Remove the solenoid piston/actuator fork/gear assembly from the main housing.
20) Separate the solenoid actuator fork/gear assembly from the solenoid piston.
21) Using paper towels, clean out the bore of the solenoid body and the outside surface of the solenoid piston.
22) Disassemble the three planetary gears and the ring gear from the actuator fork/gear assembly (the parts are loose-fit into the assembly). Using paper towels, clean the surfaces of the gear housing that hold the gears. Using a cleaning solvent, clean the three planetary gears and the ring gear.
23) Clean the surface of the pinion gear shaft using a paper towel.
24) Thoroughly clean the aluminum main housing using a cleaning solvent. Make sure to clean between the pinion shaft seal and the pinion shaft bushing, both of which are pressed into the housing. (Please note that, per my local VW dealer, neither the pinion shaft bushing nor the pinion shaft seal are available as repair parts.)
25) Using a good multi-purpose grease (I used Kendall Super Blue), lubricate the three planetary gears, the ring gear and the gear-mounting surfaces in the gear housing. Reassembly these parts together.
26) Using the good multi-purpose grease, lubricate the pinion gear shaft.
27) Reattach the pinion shaft/gear assembly to the solenoid piston.
28) Reassemble the pinion shaft/gear assembly/solenoid piston into the aluminum main housing.
29) Slide the solenoid body onto the solenoid piston.
30) Reattach the solenoid body to the main housing using the three six-lobe screws. Torque them as per how they were torqued when they were removed.
31) Reassemble the starter body to the main housing and attach it with the two long screws.
32) Reassemble the starter to the vehicle.
33) Take time to clean the battery terminals and the battery clamps using a baking soda and water mixture. Rinse the terminals and clamps thoroughly with clean water to remove any baking soda residue. Dry the terminals and clamps with paper towels. Lubricate the battery terminals with dielectric grease to prevent future corrosion build-up.
34) Reassemble the vehicle in the reverse order as the disassembly.
35) Reset the radio stations and the clock. Please note that the trip odometer will have been reset to 0.0 miles and cannot be changed.
Given that the price of a new starter from the dealer is well to the North side of 300 USD, it is well worth the time and effort to perform this maintenance. Since the starter pinion shaft seal is not available as a repair part, we can expect that the need to perform this maintenance will be more frequent as our vehicles age. It is not a difficult task. It does take some time, but it is rather straightforward. Allow yourself an afternoon to do this servicing. (Make sure you have the tools and servicing materials on hand first--you won't be able to drive anywhere while your car is apart!)