I have a 90 Jetta with the same kind of condition. It was running okay, then I let it sit over a summer. Next fall I wouldnt crank over. If I connected a wire from the solenoid on the starter motor to the positive terminal of the battery and had the ignition turned on - I could get the car to crank over and start up.
It sat for another summer, and the next year it wouldnt start - because the fuel pumps werent running. They should come on for the first 1.5 seconds after you turn the ignition key to the 'run' position. There are two of them, and I think both of them need to work for proper operation. One is in the fuel tank, the other one is under the passenger side back seat bottom - visible from underneath.
I think mine now has some reluctant relays on the panel above the driver's left foot, but I havent had time to follow the wires and check for voltage in the right places.
If you dont have the Bentley manual you should get it; I
see them on ebay, and I think the manual is still in print. I have never seen factory manuals for the Jettas anywhere. The Haynes and Chilton's manuals are less specific than the Bentley manual, and even the Bentley manual takes a lot of study to try and understand what the electronics and the relays are doing.
There should be a fitting on the end of the fuel rail, on the driver's side of the engine. If you remove its screw you can turn on the ignition and fuel should squirt out. (So only do it where they is no open flame). Also dont drop that little bolt, its not an easy size to find; being metric and tiny.
Good luck, and if you have success, I would like to hear about it.
And getting to the starter to remove it on the Jettas with the automatic transmission is a bear of a job! I removed mine to see if it was the problem, and it wasnt. Took an entire day, and in mild weather at that.