If you have the situation where system cron is executing Magento’s cron.sh, but tasks are not being scheduled or run, then it might be because there is a previous execution of magento’s cron.php script which is sleeping (in the example below, it’s in status ‘S’ – interruptible sleep [waiting for an event to complete]).
This process may have to be killed to allow the next scheduled Magento cron to be able to run, as cron.sh checks for already running processes and won’t run a new one if it finds any.
Ideally one should then investigate the logs to establish what may have caused the process to hang in the first place.