$request is a member variable of the theme class you are using, so it
is more commonly used in one of the theme's templates. If you do use
it in your theme.php, it would need to be refer to in the form $this-
>request->*type of page requested*.
http://wiki.habariproject.org/en/User:mikelietz
lists the built-in page types that can be attributes of the $request
object.
For the 'about' example you gave, code similar to
<?php if ( $request->display_home && $post->slug == 'about' ) { ?>
<p>We're on the home page, Bob!</p>
<?php } else { ?>
<p>Help! I'm being held captive!</p>
<?php } ?>
should work.
Rick