I am presently fiddling with Balanivash's awesome answer on ajaxifying WordPress search.

The issue In my opinion happens because the Request URL is http://lyrics.bfeely.com/search.php?s=santa, after i believe it ought to be with no search.php to operate. However I am much less sure how or maybe that's possible (same origin policy?)

You can try the slightly modified jQuery below in the lyrics site I am focusing on.

$("#s").keyup(function(e){
            e.preventDefault();
        var search_val = $(this).val();

        $.get("/wp-content/themes/lyrio/search.php",{s:search_val},function(data){
            if(data.length>0){
               $("#search-results").html(data);
           }
        });
    });

I am not really too familiar with javascript and so i apologize ahead of time if any terminology is not right. I'm going to be pleased to provide any extra info if you would like, you may also visit the site on your own if you wish to take a look at the source.

Thanks!!