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My suggestion would be to back up your playstation files first.. Then, repair the file system as follows
try restore file system first..
T hen once the ps3 boots try the firmware update.. If it wont take.. Go back to the recovery menu, and now try rebuild database.. this will take longer.
Then, once thats complete try the firmware update again.. If that fails, then finally try restore ps3 system ( but make sure you have backed up your saved game data off the ps3 first, as restore file system will wipe your drive and saves.
After it restores, try the firmware update again.
If you get stuck or run into any issues, let me know.
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It may not like the format of the USb memory stick you are using.
Or, and ive seen this happen before. It could even be your ip address / home wifi that is corrupting the download.
This is what Id try.. Try to connect to a different internet connection then your home connection and download the update from the other connection. For instance, take your PS3 to a friends house, and try to download the firmware update there. And then attempt the install.
When you've had a chance to try this, let me know.