Ok, so after deleting wp-content, wp-admin & renaming plugins & themes folders and uploading these again from the .zip, I can upgrade the database using /wp-admin/upgrade.php, but still get error messages trying to visit the blog or trying to access the admin:
Notice: register_sidebar_widget is deprecated since version 2.8! Use wp_register_sidebar_widget() instead. in /customers/michieldoetjes.nl/michieldoetjes.nl/httpd.www/wp-includes/functions.php on line 3237
Notice: register_widget_control is deprecated since version 2.8! Use wp_register_widget_control() instead. in /customers/michieldoetjes.nl/michieldoetjes.nl/httpd.www/wp-includes/functions.php on line 3237
Warning: Cannot modify header information - headers already sent by (output started at /customers/michieldoetjes.nl/michieldoetjes.nl/httpd.www/wp-includes/functions.php:3237) in /customers/michieldoetjes.nl/michieldoetjes.nl/httpd.www/wp-includes/pluggable.php on line 890
Any ideas on what might be wrong?