Can't upgrade plugins automatically, class not found

On trying to update plugins, I get a screen that has the left nav of the dashboard, and “Updating plugins” in the main section, but nothing happens. On checking the logs, I found the following:
PHP Fatal error: Class 'Plugin_Upgrader' not found in /home/efi/blog/wp-admin/update.php on line 43

I’ve checked the permissions on the file and they’re the same as the other class files in that directory (so I think I’d probably be getting errors all over the place if none of the class files could be read). I’ve tried reinstalling 3.2.1 but that gave me a white screen with the following error in the log:
PHP Fatal error: Call to undefined function wp_dashboard_setup() in /home/efi/blog/wp-admin/index.php on line 15

Fortunately I had backed up my blog directory before doing the reinstall, so my blog is at least still up.

Suggestions as to what to try next?