Hi!
Is it the 500GB model with HDD? Or the 12GB model?
Anyway, it's possible that your HDD is broken and need to be replaced.
First I would try to format the HDD and reinstall it and see if that works or not. If not, please replace the HDD and reinstall the software.
Software can be found here: [link|https://www.playstation.com/en-us/support/hardware/ps3/system-software/|How to update PS3 console system software|new_window=true] (please scroll down and see the manual).
Be aware that the USB drive need to be FAT32 formatted.
If you have any questions, please let us know!