PSN ID's do not change like that, they are locked to a unique email address.
You have probably encountered a frazzled hard-drive that will need to be re-installed with the Firmware again.
In order to install the PlayStation 4 system software please follow these steps:
1. Using a PC/Laptop format a USB storage device to FAT32.
2. On the USB storage device, create folders for saving the update file. Using a computer, create a folder named "PS4". Inside that folder, create another folder named "UPDATE"
3. Download 850mb Firmware file : ^^^^ link at top.
4. Select the option at the bottom of the page titled “Perform a new installation of the system software”. ***Really important***
5. Download the system file using the link in the article, and save it in the "UPDATE" folder you created in step 2.
6. Save the file with the file name "PS4UPDATE.PUP".
7. Turn off the PlayStation 4 by pressing the power button on the front panel. The power indicator will blink for a few moments before turning off.
8. Once the PlayStation 4 is off, press and hold the power button. Release it after you've heard two beeps: one when you initially press, and another 7 seconds later.
9. Connect the DualShock 4 controller with the provided USB cable and press the PS button on the controller.
10. Select option 7 - Initialize PS4 (Reinstall System Software) - IMPORTANT: Deletes all information on the HDD, including the System Software. A message that states a USB storage device containing the System Software must be connected, is displayed. Then you can confirm the selection.