Wow! " .... no cronjob running ...". Are you sure?
Where are you hosted?
Site administration
Server
Tasks
Task processing
Enable cron - default is yes.
Says:
Cron should normally be enabled, however this setting allows it to be disabled temporarily, for example before a server restart. If disabled, the system is prevented from starting new background tasks. Note that the cron should not be disabled for a long time, as this will prevent important functionality from working.
Site administration
Security
Site security settings
There is an option to run cron via web browser if you setup a password to be able to do so.
If it hasn't been running at all, I'd be a little hesitant to do above during primetime usage of site ... could be a lot of cleaning up/catching up your server needs to do!
Automated backups can be scheduled ... and I'd advise setting the directory to where those backups are saved outside of the sea of files in moodledata/filedir/ but kinda risky not knowing how many courses and how large those course backups might be (free space).
Do double check that cron is indeed running successfully!
'SoS', Ken