As much as I like older VWs (I drove a '79 Scirocco for 3 years, followed by an '83 GTI for 13), I’d either look for the best example of an '84 I could find, or get something much newer/safer/faster. But if you’re really curious, and have the VIN, then a few bucks spent on Carfax might satisfy your curiosity. I don’t know if just the VIN is enough, though.
If you’re in real tight with your insurance agent there’s also a possibility that the agent could run a trace on the VIN; assuming you still have a record of that VIN or can get one.
If the car is ever found then the real battle may begin; sorting out CIS fuel injection problems. 
You wont find it. Search for a 1984 Scirocco and fix that up.
If I had the time and money I’d get a 67 Catalina that belonged to my grandparents. It would mean the same.