How to put a PS3 super slim hard drive into a new console? [duplicate]

A while ago, my PS3 completely broke. Every time I turn it on, it just completely shuts down a few seconds later. I decided to buy a new ps3 to play my old games. The problem is that I don't have my saved data, but I still have the original hard drive. Is it possible to somehow transfer the saved data from the old hard drive to my new PS3? I was thinking maybe I could clone the hard drive, but I don't have a spare hard drive to do it on. I do however have a 2 TB external hard drive. Would it be possible to clone it on the external? Are there any alternative methods?

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.