If you have control over that external web server...

getip.aspx:

< %@ Page language="c#"  % >< % 
    Response.ContentType = "text/plain"; 
    Response.Write( Request.UserHostAddress.ToString() );
% >

getip.cs (command line example program)

using System;
using System.IO;
using System.Net;

public class GetIpApp
{
	static void Main()
	{
		WebClient client = new WebClient();
		
		try {
			string strMyIp = client.DownloadString( "http://localhost/getip.aspx" );
			Console.WriteLine( "IP Address is: {0}", strMyIp );
		}
		catch( Exception ex ) { Console.WriteLine( ex.ToString() ); }
	}
}

If you were to try this on your own PC (as I've written) you'd get 127.0.0.1 as the IP address but on a remote server the firewall's IP would come back.

If you don't have the ability to put a page of some sorts on the remote server, you're stuck. There is no way your client PC can get this information, short of doing a traceroute and guessing.