vw:

Per the trouble shooting chart in the FSM there are three possible causes for not up-shifting past 2nd:
1) Selector sleeve detached. [Not likely if you can shift into N,R, & P]
2) Jammed 2-3 command valve.
3) Low governor pressure.

Does the speedometer work correctly, or does it skip and/or fluctuate?
Improper speedo operation and low governor pressure are linked. Both the speedo gear and the governor are stacked on the output shaft, and clamped by the nut that secures the three-legged output flange on the shaft. If the three-legged flange wears a bit, and clamping force is lost, then both the governor and the speedo gear are free to not turn with the shaft.