How to check whether a port is open at client's network/firewall?

Gotcha !!! I have solved my problem with JSONP and jQuery AJAX call. I discovered the timeout attribute of jQuery AJAX and my code executed fluently when the port was blocked or opened. Here is the solution for future visitors. Thanks to all answerers for contribution.

<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
<html>
    <head>
        <meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
        <script type="text/javascript" src="jquery-1.7.2-min.js"></script>
    </head>
    <body>
        <script type"text/javascript">
            var isAccessible = null;
            function checkConnection() {
                var url = "http://101.212.33.60:1935/test/hello.html" ;
                $.ajax({
                    url: url,
                    type: "get",
                    cache: false,
                    dataType: 'jsonp', // it is for supporting crossdomain
                    crossDomain : true,
                    asynchronous : false,
                    jsonpCallback: 'deadCode',
                    timeout : 1500, // set a timeout in milliseconds
                    complete : function(xhr, responseText, thrownError) {
                        if(xhr.status == "200") {
                           isAccessible = true;
                           success(); // yes response came, esecute success()
                        }
                        else {
                           isAccessible = false;
                           failure(); // this will be executed after the request gets timed out due to blockage of ports/connections/IPs
                        }
                    }
               });
            }
            $(document).ready( function() {
                checkConnection(); // here I invoke the checking function
            });
        </script>
    </body>
</html>

I don't think you understand the use cases for JSONP and it's not possible to test open ports with it. http://en.wikipedia.org/wiki/JSONP

If you want a client side solution it could be possible with websockets, but this is only available on new browsers like chrome or ff. Otherwise request a server side script which does the ping. For example - with a curl script: curl and ping - how to check whether a website is either up or down?