Keep a single category OFF the homepage

To make sure I understand: You want all articles for one category to show their title on the main page, just not their article itself?

You could do that with some customization of The_Loop in your theme’s index.php. Something like:

<?php while (have_posts()) : the_post(); ?>
<!-- Change 18 to your category ID you want to treat differently -->
<?php if ( in_category('18') ) { ?>
<div class="postTitleOnly" id="post-<?php the_ID(); ?>">
<a href="<?php the_permalink() ?>" rel="bookmark" title="Permanent Link to <?php the_title(); ?>"></a>
<?php } else { ?>
<!-- Normal Loop stuff goes here. Theme specific. -->
<!-- in other words, just use what you already have -->
<?php } ?>