This is solved at last with \"timeout\" attribute of jQuery AJAX (and JSONP). See my own answer !
Please see the updated part, I
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?