Can I transfer saved data from my old PS3 hard drive to my new PS3?
The PS3 console hard drives are encrypted with a per-console key, meaning that the data cannot be recovered without the console key.
The only option to get your data back would be to install Custom Firmware (CECH-25XX or lower) or Hybrid Firmware (any), fetch the encryption key while the console is running and using it to mount the hard drive on Linux. Because your console turns of a couple of seconds after turning on (known as Blackout), you can't recover the key to access the drive.