What we talking about here?
1983 MK2 or 2001 MK4?
As I think you're talking MK2,hit Ebay or a breakers and find a complete MK4 GTI/Audi S3 AMK/BAM code 1.8 20valve turbo engine.You'll also need the dash cluster and ingnition barrel as I believe that these are integral to the immobiliser system.
The alternative would be to go out and buy a car with the 1.8t fitted...less hassle and probably less cost!
HTH.