is there a way to show private pages to non-logged in users

The solution is to switch that page back to “publish” and exclude it from your menu … unless I am missing something obvious.

It depends how your menu is being generated. If it’s wp_list_pages, you can use the ‘exclude’ parameter to exclude specific page(s):

http://codex.wordpress.org/Function_Reference/wp_list_pages#Exclude_Pages_from_List

If you’re using the WP 3.0 custom menu system, it should be even easier. Just delete that page from the menu.

Know it is possible using the new plugin “show-private” !
http://wordpress.org/extend/plugins/show-private/