What used to kill those cars was one of 2 things.
Timing belt. Break it and valves hit pistons, etc, etc. some imes just rebuilding the head will fix it.
Head Gaskets. Look for a coolent leak at the head/block junction. If its leaking coolent, sometimes it gets run low on coolent and overheats, which does a job on the rings/bore. (I bought one that had been overheated but I did not know it. It would drink 1 qt of oil every 1000 miles. )
First I would inspect the timing belt to make sure its OK to run it some.
As others have said, check the fuel line between the tank and pump. Even check the steel lines for a leak.
It will not stop it from running, but Check the rubber hoses between the injectors, only replace them with rubber line for diesel fluid.
Maybe a plugged fuel filter? I would run what fuel is in the the tank through, then replace the fuel filter because its probably got slime in it.
Here is where I buy my VW parts.
EDIT: I remembered where to get all the information you need. This is just an email list, no web access, but tons of knowledge on the older VW diesels on it.
click here