The problem was that it was not possible to login to a WordPress website, to the admin dashboard I mean.
I tried many things:
- used scripts to reset the password. They actually change the pwd in the wp_user table. See below an example of update command used to change pwd.
- deleted cache plugins after having zipped them
- deleted cache folder, /wp-content/cache
- deactivated wp super cache plugin, which I had deleted before, by updating the option active_plugins in the table wp_options
- deleted anything related to caches in wp-config.php
- disabled all plugins by renaming the folder /wp-content/plugins
- enabled debugging
What worked was an upgrade from WordPress 3.9.1 to 4.4.2.
I used these instructions: https://codex.wordpress.org/Upgrading_WordPress_-_Extended_Instructions
UPDATE `wp_users` SET `user_pass`= MD5('yourpassword') WHERE `user_login`='yourusername';