I'm wondering if this error message means that your system won't boot anymore because the hard drive is full—for example, because it's been filled with logs. If there's no more space available for writing, it won't boot properly.
Unfortunately, I don't know what might help you right now.
You could try booting from a Zorin USB drive in “Try Zorin” mode and then running the Baobab program (=disk usage analyzer) to see if the drive is full.
If the logs are the culprit, limit the size of the logs first.
You probably must do this in the root shell prompt, but I'm not sure how to proceed in your case.
Unfortunately there are only few helpers at the moment in the forum, perhaps because of the heat.