Hi,
I just tested.
If the target framework is less than 4.0 then it is not returning the xml file.
I'm using SharpDevelop IDE with .net Fx 4.0 and it is working fine.
You can try with SharpDevelop also but it does not have all the features of Visual Studio. 

see what I'm using:
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static void Main(string[] args)  
  {  

      CookieContainer cookies = new CookieContainer();
          HttpWebRequest request = (HttpWebRequest)HttpWebRequest.Create("http://www.ligatestowanba.ligspace.pl/index.php?pa=Admin&mod=Users&ac=Login");  
      request.Method = "POST";  request.CookieContainer = cookies;
     string loginData = String.Format("username=testtest&password=awdsa");
     request.ContentType = "application/x-www-form-urlencoded";
     byte[] loginDataBytes = Encoding.ASCII.GetBytes(loginData);
    Stream postData = request.GetRequestStream();
    postData.Write(loginDataBytes, 0, loginDataBytes.Length);  postData.Close();
    HttpWebResponse webResp = (HttpWebResponse)request.GetResponse();
    StreamReader loResponseStream = new StreamReader(webResp.GetResponseStream());
   string HelpResponse = loResponseStream.ReadToEnd();  
 HttpWebRequest req = (HttpWebRequest)WebRequest.Create("http://www.ligatestowanba.ligspace.pl/index.php?pa=Admin&mod=AdminCms&ac=ExportData&download=teams");
   req.CookieContainer = cookies;  req.Method = "GET";  
   HttpWebResponse res = (HttpWebResponse)req.GetResponse();
   Stream resStream = res.GetResponseStream();
  StreamReader reader = new StreamReader(resStream);  

   string input = reader.ReadToEnd();  

Console.WriteLine(input);  

Console.ReadLine();

}

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and I get this in my console:

my input string looks that: (the same as HelpResponse - string) - why??