In this post, I describe how I fixed the error:
The file system on the system storage is corrupted and will be restored.
This error occured when turning on my Playstation 3. The restore process took hours and when I returned to check it, the same error appeared.
Resolution
To resolve the issue:
1. Hold the Playstation 3 power button down until it beeps once, then once again, then twice. Release the power button when following message is shown:
2. Connect the controller using a USB cable, and then press the PS button to enter Safe Mode:
3. I was happy to lose my data so I selected 5. Restore PS3 System.