Seems like this works. I've tried it from a web page, so it should work the same form a Windows form.
Dim h As System.Net.IPHostEntry = System.Net.Dns.GetHostByName(System.Net.Dns.GetHostName)
Response.Write("IP Address = " & (CType(h.AddressList.GetValue(0), System.Net.IPAddress).ToString))
Console.WriteLine will do instead of Response.Write for windows form.