Fixing a 1989 vw cabriolet convertible

Perhaps you should start with a compression check.

if it has direct injection that is the only problem area. a car can start with a bad head cover gasket its job is mostly just to keep the oil in the cam area. the way i check stuff is ussaly air flow, compression spark, and then fuel. and that intails anything in those fields. Also if the car starts to idle poorly its likely the idle control valve they ussaly end up waring out after a while. the most popular trouble areas to check would be distributor, fuel injection assembly/ and or Carburator, fuel pump and filter, idle control valve, coil, and valve cover gasket. some other things to check would be vacum lines and the battery ports and grounds.