I recently upgraded Drupal to version 6.14 and went to run the database update as the instructions stated. When clicking the link, update.php only showed a blank page.
This is because errors on this page are hidden by default. In order to diagnose your problem, you’ll need to edit update.php and change the following line:
Try running update.php again and you should be displayed with an error message.
In my case, the errors I received looked like this:
Warning: include() [function.include]: Unable to access ./themes/garland/maintenance-page.tpl.php in /var/www/vhosts/example.com/httpdocs/includes/theme.inc on line 1020
It appears that Drupal still references the Default theme Garland which I had deleted from the server to save space. Once I’d reinstated this, the errors disappeared and I was able to run the database update.