Crons not working

I’m using the latest Apache and PHP 5.2.17 on RHEL.

Crons are not being executed on a fresh installation of WordPress 3.2.1. I have followed this guide: https://codex.www.ads-software.com/Function_Reference/wp_schedule_event and set the do_this_hourly function to send an email using both mail() and wp_mail() functions. I have added these to my themes functions.php.

I have tried to the following with no luck:
-load https://domain.com/wp-cron.php through my browser after clearing cookies
-crontab: wget -qO- https://domain.com/wp-cron.php
-crontab: cd /var/www/vhosts/domain.com/httpdocs && /usr/bin/php -f /var/www/vhosts/domain.com/httpdocs/wp-cron.php

Further investigation and testing on different systems and configurations led me to the same result that these crons are not working. In fact, on more tests, I purposely installed a combination of lower version of wordpress or of a plugin to see when/if updates are checked. Some progress to be noted here, only upon viewing the dashboard does wordpress check for updates, navigating directly to other areas does not prompt new version availability.

I have also tried all of the above separately with WP_DEBUG set to true and ini_set(‘display_errors’,’On’) in wp-config.php.

Therefore, I have come to the conclusion that WordPress is broken. Bold, I know. I fear that those with the technical capacity to notice crons not functioning correctly are those who use WordPress on a corporate level, and they are more likely to upgrade from version to version, rather than install completely a new version, which only anal amateur would do in my opinion. I believe upgrading may have avoided a ‘fault’, if one existed.

Does anyone have any ideas on how to debug this further?