If you do indeed have the usb-sata cable, plug the hard drive back in, and wipe the drive to remove all partitions, and don't format it afterwards - the PS3 will handle that. Once that's done, plug it back into the PS3 and see if it boots up to a "firmware not found" screen. If so, download the firmware from Sony's Website, copy it to a USB
On your PS3, navigate to the Settings column and select System Settings → Backup Utility → Backup. After it is done backing up, remove your external storage device and plug it into your PC. Turn off your console, remove your old internal hard drive from the PS3, and insert your new hard drive. Start your console.
Manually eject a disc from a Slim Playstation 3 that has no power due to ylod yellow light of death or bad power supply. This is how you can rescue any trapp
In this video, I will show you how to Upgrade PS3 Hard Drive Super Slim in a very simple way. You can find more details in this article:
Screw back in the blue screw and put the small cover back on the PS3. Super Slim PS3 systems. Taking out the old HDD. Put the PS3 vertically, with the PS3 logo on top, facing you. Push and slide the black cover gently to the left. Remove the blue screw. Pull out the tray with the HDD. Unscrew the 4 screws. Slide the HDD out of the tray.
This video shows you how to replace the hard drive specifically on a PlayStation 3 slim. The method for opening up your PlayStation 3 to remove the hard drive might be different for you
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how to remove ps3 slim hard drive