Mark Rendle posted this as a comment, I wanted to post it as an answer since it's the only solution that has worked so far to return the success and the error-codes json results from the Google reCaptcha response.
string jsonReponseString= wClient.DownloadString(requestUrl);
IDictionary<string, object> dict = new JavaScriptSerializer().DeserializeObject(jsonReponseString) as IDictionary<string, object>;
Thanks again, Mark!