Jquery script not loading on site Front page

WordPress uses jQuery noConflict wrappers so the dollar sign will not work unless it is used as an alias. Either wrap your code in:

 jQuery(document).ready(function($) {
// Inside of this function, $() will work as an alias for jQuery()
// and other libraries also using $ will not be accessible under this shortcut
});

Or just change all the dollar signs to “jQuery”.
Also you should alway enqueue your scripts even if they are tiny.

More about it here:
http://codex.wordpress.org/Function_Reference/wp_enqueue_script