If you call Reimers.Map.Geocoding.GoogleGeocoder.Geocode and pass in the address you have then it will return a GoogleResult object where you can find the geocode results in. The results should contain the zip code even if you didn't pass it in (assuming that Google was able to geocode the passed address).
The address object that you pass to the geocode method doesn't have to be complete. Fill it in with as much as you can and let Google handle the rest.