Just to summarize all the places to look. If you've chosen to try to run CiviCRM cron from Drupal, you need the civicrm_cron module. Then in the Elysia Cron settings: admin/config/system/cron/settings take a look at the settings for the civicrm_cron job and make sure it's enabled. It's probably called: civicrm_cron_cron. Though if you're seeing civicrm_cron in watchdog then it's being called.
The next step is to check that you can manually run cron by executing the cronjob by entering the url for the cronjob in the url (with the site key set in civicrm.settings.php), by using a drush command, or by clicking the Execute Now button next to the scheduled job in Administer > System Settings > Scheduled Jobs. Make sure those scheduled jobs are enabled and have a frequent enough schedule. (More info here: http://wiki.civicrm.org/confluence/display/CRMDOC/Managing+Scheduled+Jobs#ManagingScheduledJobs-Command-lineSyntaxforRunningJobs).
If the scheduled jobs are working but still not being called from Drupal, then you may want to see if you're able to get them to run via third-party cron service such as EasyCron and create a cronjob such as
*/15 * * * * wget -O - -q -t 1 'http://mysite.org/sites/all/modules/civicrm/bin/cron.php?name=username&pass=password&key=site-key'.
I'm also running CiviCRM 4.4.14 on Pantheon and I'm using an external cronjob to call Elysia Cron and it's triggering CiviCRM cron. So I know that in general it should work.