I would suggest checking the PHP error log to see if there’s anything awful going on, and perhaps combining all of those css files into one file.
The WP-Devel plugin from the repository is decent for seeing things like PHP Errors, query times, and a lot more.
Make sure you include wp_footer(); That’s where it is now.
You have to include wp_footer();
D’oh.
Just a quick note-when I enqueue jquery-ui-core I do get jquery itself in there (the new 1.7.1) but still no core.
Maybe it’s renamed.