These cars are so simple with regards to engine management, and need so little to actually run (especially a '98).
Here is what I would do:
Connect a scan tool, access the Engine controller (with the key on, you should be able to communicate with it.... if not... you have a problem)
Assuming you can connect, go to the engine data, and find a block that shows engine RPM.... then watch that while you crank the engine. If the value goes up, and shows cranking RPM (whatever that may be... 200-400 ?), then at least you know these two important things: the ECU is "alive" while cranking, and it "sees" the engine cranking. This is a VERY simple step to take.
If the ECU is not staying live during any of this, then you need to find out why. If it does stay live, but you see no cranking RPM, you need to find out why.
Pretty much everything else is simple mechanical old fashioned VE pump diesel. A stop solenoid on the pump. ON = engine runs, OFF = engine not run.
Ignition switches were common failure items on these cars, and often the ignition switch would lose the "run" contacts while in the "crank" position. So if you have the ECU working, the data up, and when you go to crank the car the scan tool suddenly loses communication with the ECU, then that is a good sign the ignition switch is bad.
Warning: tearing the steering column apart to replace the ignition switch is not a big deal, BUT, unlike most cars (including all newer VAG products), the A3's clock spring for the airbag is not attached to the column switches... it is attached to the bottom of the steering wheel..... you need to unplug the clockspring connector BEFORE you remove the steering wheel, or you'll break the clockspring to pieces and you'll have an extra expense to deal with.