Yes, I would hope that you couldn't get it client-side for the reasons that Josh pointed out. My machines IP address is not its broadcast address. But... try this.

And forgive me, I never use VBScript for client-side scripting, so you will have to translate from JavaScript to VBScript.

Code:
<html>

  <head></head>

  <body>

    <script language='JavaScript'>
      var clientIP = <%=Request.ServerVariables("REMOTE_ADDR")%>;
    </script>

  </body>

</html>