Ultimately what worked is the following:
using (WebClient wc = new WebClient())
{
System.Collections.Specialized.NameValueCollection reqparm = new System.Collections.Specialized.NameValueCollection();
reqparm.Add("oauth_token", oauth_token);
reqparm.Add("venueId", venueId);
byte[] responsebytes = wc.UploadValues(URI, "POST", reqparm);
string responsebody = Encoding.UTF8.GetString(responsebytes);
}
Thanks everyone for your help!