Any error messages starting with “SQLSTATE[HY000]” relate to an output message directly from MySQL. That fact that a customer was able to see this message suggests that you might not have your store in Production Mode as most error messages are hidden.
Normally, if your Magento Root Directory is getting very large very quickly then it’s your log files filling up with errors. You’ll want to read your logs files in <magento_root>/var/logs/
To answer your question about Cron, check these:
- Cron Jobs - How do I check if they are working or not?
- How to diagnose and fix Ownerships and Permission issues (Section: How to fix cron tasks)