[jQuery] Form function no firing

[choffman]

Hi There,
I could use some jquery help here.  Its probably something very simple
that I'm missing.  I started using jquery a few weeks ago so please
bear with me.

In a nut shell, when a user submits the form (form id="register"), I
want it check to make sure they have selected a radio button
(class="amount").  If they forgot, I want it turn the #billing id (<h2
id="billing>) red.   I have server side validation working using PHP.
This is more of a visual indicator. I'm using the validate.js plug-in
and jquery 1.2.1.  Any help would be great!

$(document).ready(function() {
        $("#register").submit( function() {
                checkRadio();
        });

        function checkRadio() {
                $('input.amount').each(function() {
                        if ($('input:unchecked')) {
                                $("#billing").css('color', '#658300').show();
                                return true;
                        } else {
                                $("#billing").css('color', '#C60006').show();
                                return false;
                        }
                });
        //close function
        };
});