Yes, I did that, but I could not completely remove the ‘w3tc’ folder. When I reactivate the plugin there is an error message saying something like ‘Fatal error occured while activating the plugin. Unable to write into the configuration file’, which is w3-total-cache-config.php.
To add some information, current chmod for each directory described is 644 and cannot be changed either via Total Commander or via CPanel’s built-in file manager.