Submitting a form, using Ajax, to run a SQL Select query based on user input from the form

you should use e.preventDefault() instead of return false;

$form.submit(function(e) {
    e.preventDefault();
    do_search();
});

Hata!: SQLSTATE[HY000] [1045] Access denied for user 'divattrend_liink'@'localhost' (using password: YES)