[Jeff2]

It sounds to me like you have a problem with the alternator not charging the battery. This could be a problem with the alternator. You can pull the alternator and have a parts store test it, usually for free.

But, since your problem is intermittent, this could also be a wiring problem. Check not only the positive wire(s) which go from the alternator to the battery, but the fuse box on top of the battery, and all of the "major" grounds on the car (battery to chassis, to engine, and etc.). There is a ground under the battery tray which tends to go bad on these cars (stupid place to put it, really).

 

[Jeff2]

One more thing to check... When was the last time you changed your timing belt and the accessory belt? If the accessory belt is worn and slipping, the alternator won't be operating as it should, especially at idle.

 

[Jeff2]

A "clicking" starter; typically means a low battery but it could be a dying starter as well. I would charge the battery and drive the car down to a parts store, for a complete charging system evaluation/test.

As for the ground; here is a tech bulletin, updating the grounds, that show the locations of the grounds, under the battery tray (which will need to be removed).

Volkswagen Workshop Manuals > New Beetle GLS L4-2.0L (AZG) (2002) > Powertrain Management > Ignition System > Ignition Coil > Component Information > Technical Service Bulletins > Customer Interest for Ignition Coil: > 0108-27 > Oct > 08 > Electrical

I'd personally attack the ground(s) first. That said, I've had cars with the "intermittent starter only clicks" problem caused by a bad connection on one car and by a starter going bad on another. If you do take the starter to a parts store for testing, have them test it two or three times. Sometimes the bearings in a starter will go bad and the car will refuse to start when the bearings are hot. Running the test multiple times will insure that any bad bearings in the starter will heat up and actually fail the test.