Hide logo on splash page

I’m working with a pretty cool theme right now that uses a splash page. I would like to hide the logo only on the splash page. The splash page (page-splash.php) runs header.php which houses the logo. I think I will need to edit header.php and that’s what I need help with…

HERE‘s the site.

Here’s the logo section of header.php:

<div class="logo">

          <?php if(of_get_option('logo_type') == 'text_logo'){?>

          	<?php if( is_front_page() || is_home() || is_404() ) { ?>
              <h1><a href="<?php bloginfo('url'); ?>/" title="<?php bloginfo('description'); ?>"><?php bloginfo('name'); ?></a></h1>
            <?php } else { ?>
              <h2><a href="<?php bloginfo('url'); ?>/" title="<?php bloginfo('description'); ?>"><?php bloginfo('name'); ?></a></h2>
            <?php } ?>

          <?php } else { ?>

          	<?php if(of_get_option('logo_url') != ''){ ?>
            	<a href="<?php bloginfo('url'); ?>/" id="logo"><img src="<?php echo of_get_option('logo_url', "" ); ?>" alt="<?php bloginfo('name'); ?>" title="<?php bloginfo('description'); ?>"></a>
            <?php } else { ?>
            	<a href="<?php bloginfo('url'); ?>/" id="logo"><img src="<?php bloginfo('template_url'); ?>/images/logo.png" alt="<?php bloginfo('name'); ?>" title="<?php bloginfo('description'); ?>"></a>
            <?php } ?>

          <?php }?>
        </div>

Anyone have advice?

Thanks!