Hey,
open up header.php and replace following code:
<!-- end center-->
</div>
<!--end wrapper-->
</div>
with:
<!-- end center-->
<?php
if (!(is_single())){
echo '<img src="my.image.jpg" alt="" title="" />';
}
?>
</div>
<!--end wrapper-->
</div>
You can use any conditional tag you like: http://codex.wordpress.org/Conditional_Tags
I excluded all posts in this example. So replace !(is_single()) with any conditional tag you want to use. Obviously you need to replace "my.image.jpg" with the path to your image...