Working on breadcrumbs for a WordPress theme. Attachments may belong to either a post or a page, and I would like them to appear accordingly in my breadcrumbs.

This is the function for my breadcrumbs:

function breadcrumbs() {
 
	$delimiter = '';
	$home = 'Home'; // text for the 'Home' link
	$before = '<li class="current">'; // tag before the current crumb
	$after = '</li>'; // tag after the current crumb

	if ( !is_home() && !is_front_page() || is_paged() ) {

	echo '<ul id="crumbs" class="group">';

	global $post;
	$homeLink = get_bloginfo('url');
	echo '<li><a href="' . $homeLink . '">' . $home . '</a>' . $delimiter . '</li>';

	if ( is_category() ) {
		global $wp_query;
		$cat_obj = $wp_query->get_queried_object();
		$thisCat = $cat_obj->term_id;
		$thisCat = get_category($thisCat);
		$parentCat = get_category($thisCat->parent);
		if ($thisCat->parent != 0) echo( '<li>' . get_category_parents($parentCat, TRUE, '' . $delimiter . '</li>'));
		// echo $before . 'Archive by category "' . single_cat_title('', false) . '"' . $after;
		echo $before . single_cat_title('', false) . $after;
 
	} elseif ( is_day() ) {
		echo '<li><a href="' . get_year_link(get_the_time('Y')) . '">' . get_the_time('Y') . '</a>' . $delimiter . '</li>';
		echo '<li><a href="' . get_month_link(get_the_time('Y'),get_the_time('m')) . '">' . get_the_time('F') . '</a>' . $delimiter . '</li>';
		echo $before . get_the_time('d') . $after;

	} elseif ( is_month() ) {
		echo '<li><a href="' . get_year_link(get_the_time('Y')) . '">' . get_the_time('Y') . '</a>' . $delimiter . '</li>';
		echo $before . get_the_time('F') . $after;

	} elseif ( is_year() ) {
		echo $before . get_the_time('Y') . $after;

	} elseif ( is_single() && !is_attachment() ) {
		if ( get_post_type() != 'post' ) {
			$post_type = get_post_type_object(get_post_type());
			$slug = $post_type->rewrite;
			echo '<li><a href="' . $homeLink . '/' . $slug['slug'] . '/">' . $post_type->labels->singular_name . '</a>' . $delimiter . '</li>';
			echo $before . get_the_title() . $after;
		} else {
			$cat = get_the_category(); $cat = $cat[0];
			echo '<li>' . get_category_parents($cat, TRUE, '' . $delimiter . '') . '</li>';
			echo $before . get_the_title() . $after;
		}

	} elseif ( !is_single() && !is_page() && get_post_type() != 'post' && !is_404() ) {
		$post_type = get_post_type_object(get_post_type());
		echo $before . $post_type->labels->singular_name . $after;

	} elseif ( is_attachment() ) {
		$parent_id  = $post->post_parent;
		$breadcrumbs = array();
		while ($parent_id) {
			$page = get_page($parent_id);
			$breadcrumbs[] = '<li><a href="' . get_permalink($page->ID) . '">' . get_the_title($page->ID) . '</a></li>';
			$parent_id	= $page->post_parent;
		}
		$breadcrumbs = array_reverse($breadcrumbs);
		foreach ($breadcrumbs as $crumb) echo '' . $crumb . '' . $delimiter . '';
		echo $before . get_the_title() . $after;

	} elseif ( is_page() && !$post->post_parent ) {
		echo $before . get_the_title() . $after;

	} elseif ( is_page() && $post->post_parent ) {
		$parent_id  = $post->post_parent;
		$breadcrumbs = array();
		while ($parent_id) {
			$page = get_page($parent_id);
			$breadcrumbs[] = '<li><a href="' . get_permalink($page->ID) . '">' . get_the_title($page->ID) . '</a></li>';
			$parent_id	= $page->post_parent;
		}
		$breadcrumbs = array_reverse($breadcrumbs);
		foreach ($breadcrumbs as $crumb) echo '' . $crumb . '' . $delimiter . '';
		echo $before . get_the_title() . $after;

	} elseif ( is_search() ) {
		echo $before . 'Search results for "' . get_search_query() . '"' . $after;

	} elseif ( is_tag() ) {
		echo $before . 'Posts tagged "' . single_tag_title('', false) . '"' . $after;

	} elseif ( is_author() ) {
		global $author;
		$userdata = get_userdata($author);
		echo $before . 'Articles posted by ' . $userdata->display_name . $after;

	} elseif ( is_404() ) {
		echo $before . 'Error 404' . $after;
	}

	if ( get_query_var('paged') ) {
		if ( is_category() || is_day() || is_month() || is_year() || is_search() || is_tag() || is_author() ) echo ' (';
		echo '<li>' . __('Page') . ' ' . get_query_var('paged') . '</li>';
		if ( is_category() || is_day() || is_month() || is_year() || is_search() || is_tag() || is_author() ) echo ')';
	}

	echo '</ul>';
 
	}
} // end breadcrumbs();

The portion of that function now being called into question is this:

	} elseif ( is_attachment() ) {
		$parent_id  = $post->post_parent;
		$breadcrumbs = array();
		while ($parent_id) {
			$page = get_page($parent_id);
			$breadcrumbs[] = '<li><a href="' . get_permalink($page->ID) . '">' . get_the_title($page->ID) . '</a></li>';
			$parent_id	= $page->post_parent;
		}
		$breadcrumbs = array_reverse($breadcrumbs);
		foreach ($breadcrumbs as $crumb) echo '' . $crumb . '' . $delimiter . '';
		echo $before . get_the_title() . $after;

If the attachment belongs to a page, the breadcrumbs display perfectly.

However, if the attachment belongs to a post, the breadcrumbs omit the Category of that post, and only show as:

Home > Post Title > Attachment

What I want is:

Home > Category > Post Title > Attachment

... for attachments belonging to posts, and ...

Home > Parent Page > Child Page > Attachment

... for attachments belonging to pages.

Does anyone have a clue how I might accomplish this?