Both fans should come on and then the compressor will kick in.
My wife's '00 Jetta TDI recently had AC problems as well. It turned out to be the fan switch (also known as a thrust sensor) - it usually has a 3-wire connector on it. The fan switch was actually allowing refrigerant to leak out AND it wasn't doing it's job of informing the other components that there was enough pressure in the system. The switch is an easy swap (~$65 at the dealer) and is mounted back by the firewall on a schrader valve - so when you replace it, you don't loose any refrigerant...a WISE move on VW's part I think. I replaced the switch, added refrigerant and now the AC works really well.
There is also a fan control module mounted under the battery - this could also be bad. Be sure to check fuses as well - there are more than one that could affect the AC operation as well as the radiator/condensor fans. If the fans don't come on - the compressor won't come on.
Here are the fuse identifications (since the little card provided on the fuse panel is useless) for a '98+ New Beetle, '99.5+ Golf/Jetta/Etc.:
MKIV FUSE LIST
1. Washer nozzle heaters, glove compartment light, memory seat control module (10A).
2. Turn signal lights (10A).
3. Fog light relay, instrument panel light dimmer switch (5A).
4. License plate light (5A).
5. Comfort system, cruise control, Climatronic, A/C, heated seat control modules, automatic day/night interior mirror, control module for multi-function steering wheel, control unit in steering wheel ( 7.5A).
6. Central locking system (5A).
7. Back-up lights, speedometer vehicle speed sensor (VSS) (10A).
8. Open
9. Anti-lock brake system (ABS) (5A).
10. Engine control module (ECM): gasoline engine (10A); diesel engine, Model Year 2000 > (5A).
11. Instrument cluster, shift lock solenoid (5A).
12. Data Link Connector (DLC) power supply (7.5A).
13. Brake tail lights (10A).
14. Interior lights, central locking system (10A).
15. Instrument cluster, transmission control module (TCM) (5A).
16. A/C clutch, after-run coolant pump (10A).
17. Open.
18. Headlight high beam, right (10A).
19. Headlight high beam, left (10A).
20. Headlight low beam, right (15A).
21. Headlight low beam, left (15A).
22. Parking lights right, side marker right (5A).
23. Parking lights left, side marker left (5A).
24. Windshield and rear window washer pump, windshield wiper motor (20A).
25. Fresh air blower, Climatronic, A/C (25A).
26. Rear window defogger (25A).
27. Motor for rear windshield wiper (15A).
28. Fuel pump (FP) (15A).
29. Engine control module (ECM) gasoline engine (15A); diesel engine (10A).
30. Power sunroof control module (20A).
31. Transmission control module (TCM) (20A).
32. Injectors: gasoline engine (10A); diesel engine (15A).
33. Headlight washer system (20A).
34. Engine control elements (10A).
35. 12 V power outlet (in luggage compartment) (30A).
36. Fog lights (15A).
37. Terminal (86S) on radio, Instrument cluster (10A).
38. Central locking system (with power windows), luggage compartment light, remote/fuel tank door, motor to unlock rear lid (15A).
39. Emergency flashers (15A).
40. Dual tone horn (20A).
41. Cigarette lighter (15A).
42. Radio (25A).
43. Engine control elements (10A).
44. Heated seats (15A).
Fuse arangements in fuse bracket/battery:
S162. Glow plugs (coolant) (50A).
S163. Fuel pump (FP) relay/glow plug relay (50A).
S164. Coolant fan control (FC) control module/coolant fan (40A).
S176. Relays panel interior (110A).
S177. Generator (GEN) (90 Amp.) (110A).
Generator (GEN) (120 Amp.) (150A).
S178. ABS (hydraulic pump) (30A).
S179. ABS (30A).
S180. Coolant fan (30A).
Beers,
Matt