Error in class-wp-upgrader-skins.php on line 594

I have just upgraded to 3.8 and when I go to the Updates page I get the following:

Last checked on December 19, 2013 at 11:32 am.

You have the latest version of WordPress.

Fatal error: Cannot access parent:: when current class scope has no parent in […]/wp-admin/includes/class-wp-upgrader-skins.php on line 594

I completely replaced the entire WP install with a freshly unzipped copy, and removed all custom plugins (of which there were only two: openid and wp-recaptcha), but the above error remains.

Anyone have a fix?

Thanks!
Sam.