The car had been more-or-less mothballed for the last 4 years other than occasionally starting it to keep things from seizing. I didn't notice an issue until I decided to pull it out of the garage to drive it.

There is a constant "clicking" noise coming from behind the dash when the AC/heater blower fan is supposed to be on. When the AC/heater is set to an "on" position, there is no blower output from the vents. When I turn the AC/heater fan off, the clicking stops.

Obviously, there is a malfunction somewhere in the blower motor/fan area. Since the fan is somewhat difficult to access (especially for a non-mechanic like myself), I'm looking for ideas about a specific cause before I attempt a DIY fix or take it to an actual mechanic. Is it an obstruction? Is the fan motor shot? Any other ideas? I don't have a VAG-COM or a Bentley Manual, though now I'm looking into buying each.

 

I'm having the same problem here.
The initial cause is the water sitting in engine compartment around the ventilation system.
Remove the plastic cover on the drivers side and inspect for water.
if you have water in there it means the drains are clogged
The drains can be accessed with a long piece of wire by either trying to stick it under the black box in the center of that compartment and wiggling it around hoping you get lucky. Or jack up the car and there are two black rubber nozzles that look like the flat nozzle on a vacuum cleaner except they are made of soft rubber up along the side of the transmission.
fabricate a long piece of wire (coat hanger or home depot has masonry wire in the masons isle for tying re-bar) Shove the wire up the holes while making certain your face is directly under those nozzles, eyes wide open Just kidding!
But your are going to get very wet because it will gush out of there like a garden hose so be prepared for a five gallon surprise.

Next the issue with the blower fan...
I don't know yet, I was searching for clues to that one...before I start ripping things apart. If I find something I'll post it.