Sadly, I’m suspecting the hidden Fusion Drive cache SSD on the back side of the logic board has failed. But before you press forward try to get your data off using an external bootable drive. Hopefully you can still gain enough access to full your stuff off. As soon as you break the Fusion Drive set (SATA HDD and the Blade SSD drive) you won’t have access to the data.
Follow this guide to remove the Blade SSD [guide|15758]
Or you could replace the drive with a better Blade SSD at this point or just put the system back together and just replace the primary HDD with a SSD as the newer SSD drives are so much cheaper than what was available back in the day when this system was built. For many a single SSD drive setup is more than enough, or if you want better performance then a dual drive setup is better but you do need to manage your files to gain the full benefit of a dual drive setup.
In any case you will need to have an external bootable drive handle if you want to recover the use of the original HDD by wiping the drive down completely and then reformatting it.