I am getting a difficult time turning a publish informed right into a link. Essentially I am attempting to make the displayed posts into links. The Loop instantly shuts my <a> tags and will not allow me to turn this content of the_post() into one large link.

Here's the issue code. This most likely something simple I am just looking over.

<?php if ( have_posts() ) while ( have_posts() ) : the_post(); ?>
  <a href="#" <?php post_class() ?> id="post-<?php the_ID(); ?>">
  <h3><?php the_title(); ?></h3>
  </a>
<?php endwhile; ?>

*Edited to get rid of extraneous link. Also, this isn't valid HTML, it is simply test code for any proof-of-concept piece.

Your HTML is invalid.

Even when you desired to create the entire factor a hyperlink, where's your opening <a>? Additionally, you're closing one with every iteration.

Publish your full code.

Your markup is totally invalid. You can't come with an <h3>, or other block-level element, in a <a>, and furthermore you cannot come with an <a> in a <a>. This isn't a Wordpress problem, this is just nonsense HTML.