You cannot use AJAX if JavaScript is disabled.

Always try to write your code for non-JavaScript clients and then add AJAX afterwords.

AJAX should be used to enhance the page, it should not be...

Add this code to the head of your document (Or in an external file if you use one)

<script type="text/JavaScript">
function checkValue() {
if(document.getElementById('my_field').value ==...

If you mean the popup window that appears in your browser asking for a username and password, this relies on the htaccess and htpasswd files, was it this you are looking for or another type of login...