Help with C Sharp code

First thing you need to find out is how the search string is being processed by the the website (post/querystring). If its via querystring, all you need to do is replace to get the html stream using your search parameter in the query string eg.

HttpWebRequest request = (HttpWebRequest)WebRequest.Create("search.com?query=Hello");
request = (HttpWebRequest)WebRequest.Create("search.com?query=What");
Stream requestStream = ((HttpWebResponse)request.GetResponse()).GetResponseStream();
return (new StreamReader(requestStream)).ReadToEnd();

If its via post you'll need to set the request's method to POST, and write the search string to it's stream.
eg.

byte[] buffer = Encoding.ASCII.GetBytes("<>=Hello");
Stream requestStream = request.GetRequestStream();
requestStream.Write(buffer, 0, buffer.Length);
requestStream.Close();
requestStream = ((HttpWebResponse)request.GetResponse()).GetResponseStream();
return (new StreamReader(requestStream)).ReadToEnd();