You can edit the login form from your child themes functions.php using actions such as:
function my_login_scripts() {
//do stuff here
}
add_action( 'login_enqueue_scripts', 'my_login_scripts' );
This should at least allow you to get your jQuery running on the page.
You can read more about this here:
http://codex.wordpress.org/Customizing_the_Login_Form