You're problem is probably that you're trying to out the contents at a time when Zen Cart is trying to built a string with the content that will be output later.
From what you've written, there's also a good chance that you've inserted extra PHP tags where they're not needed.
You also haven't said where you've put your shoutbox. If the sb folder is in your site's root, you're OK, anywhere else and I wouldn't expect the file you're including to be found.
So, make sure the sb folder is in the site's root and try the following (no PHP tags)
PHP Code:
ob_start();
include("sb/shoutbox.php");
$content .= ob_get_contents();
ob_end_clean();
What this does is open an output buffer so that your content can be assigned locally to the content variable for use at the appropriate time, then closes and empties the buffer.