JQuery :: Prev / Next Buttons Will Not Work

I'm trying to implement JQuery Cycle onto the homepage of my website (which is a work in progress). I wish to have a banner with Previous and Next buttons, as well as a Pager and a Caption. I've added all of this to the banner. The Pager and the Caption works, but for the life of me I can't get the Previous and Next links to work.

This is my code:
<script type="text/javascript">
$(document).ready(function() {
$('#banner').cycle({
fx: 'fade',
speed: 'fast',
timeout: 0,
prev: '#prev2',
next: '#next2',
pager: '#nav2',
after: function() {
$('#caption').html(this.alt);
}
});
});
</script>

<div id="banner"><!-- banner -->
<img src="<?php bloginfo('template_directory'); ?>/images/banner_image_1.jpg" alt="Louvre Museum, Paris"/>
<img src="<?php bloginfo('template_directory'); ?>/images/banner_image_2.jpg" alt="Louvre Museum, Paris 2"/>
</div><!-- /banner -->
<div id="nav"><a id="#prev2" href="#">Previous Image</a> - <a id="#next2" href="#">Next Image</a></div>
<div id="caption"></div>
<div id="nav2"></div>
My website can be viewed here: [URL]