I don't think it'll be possible without server-side code, I'm afraid.
If you could use server-side code then you could curl a service like downforeveryoneorjustme and parse the response.
You could then use AJAX to find out if the page is up from your original page.
Otherwise, your best bet might be to look at jQuery's
$.ajax status codes, but I'm not suere how successful this might be.
If you need any help with the curl solution, let me know.