It sounds like you have two issues.
- Cron jobs are no longer scheduled in the cron_schedule table; and
- Cron jobs are no longer executing.
For #1, you should check whether someone changed the server configuration that called cron.sh. You want to ensure that some crontab on your system lists a command like this.
*/5 * * * * sh /path/to/your/magento/site/root/cron.sh
You can commonly find cron jobs by running commands like this. Note that you'll need sudo permissions.
echo Display system-wide crontab
sudo cat /etc/crontab
echo Display crontabs for all users on system
for user in $(cut -f1 -d: /etc/passwd); do echo $user; sudo crontab -u $user -l; done
More details available in this post.
How to configure Magento cron job