On my 81 the VIN is in 3 places: the tag on the frame covered by the driver's side door (the one you were missing); inside the windshield on the driver's side, and stamped on the top of the firewall under the lip of the hood on the passenger side of the car.
The engine number is stamped on the engine block on a flat spot just to the right of the oil filter. It is impossible to see without cleaning the area off, a bright light, and a mirror. Even then it took me about 20 minutes of number by number decoding to get it. On older models I believe it is right above the oil filter.
1974 Fiat 124 Spider
1981 Spider 2000 (sold 2013)