yoursite.com/wp-admin/upgrade.php should show me a dialog similar to:
“No Update Required – Your WordPress database is already up-to-date!”
..but yours renders a blank page.
Conversely, yoursite.com/wp-admin/includes/upgrade.php should show me a blank page, however yours renders an error message:
Warning: require_once(ABSPATHwp-admin/includes/admin.php) [function.require-once]: failed to open stream: No such file or directory in /home/xxx/yoursite.com/wp-admin/includes/upgrade.php on line 16
Fatal error: require_once() [function.require]: Failed opening required ‘ABSPATHwp-admin/includes/admin.php’ (include_path=’.:/usr/local/lib/php:/usr/local/php5/lib/pear’) in /home/xxx/yoursite.com/wp-admin/includes/upgrade.php on line 16
yoursite.com/wp-admin/includes/update-core.php should probably show me a blank page, but in this case, yoursite.com/wp-admin/includes/update-core.php shows me this error message:
Fatal error: Call to undefined function add_action() in /home/xxx/yousite.com/wp-admin/includes/update-core.php on line 1151
I’m just guessing with a lot of this, but I think you could have some type of issue with missing or possibly damaged files in /wp-admin. Again, just guessing, mind you.
Sidenote: I also noticed that directories without index files aren’t protected against casual browsing. “Options -Indexes” in your .htaccess file will be something for later exploration.
(sorry about all the tracks I left in your access logs)