More info ... version of Moodle for one.
Does site have any customized script that's attempting to use CLI?
Example: cron.php in code/admin/cli/ has this in top of the script:
require_once($CFG->libdir.'/clilib.php'); // cli only functions
Has your moodlecode/admin/cli/cron.php file been modified?
Turn on debugging. Let's see what Moodle might be complaining about that we don't know about. We need to find out what php script is being called that (according to what has been shared so far) requires reading config.php ... that file is read all the time ... by almost every click a user might make.