Basically I need a fix that will preserve the data in the ps3 because it is a family ps3.
I'm sorry to say that none is forthcoming. The file system restore doesn't always work. It depends on how much, and in what way, the file system is corrupted. When it works, it generally works fairly quickly. No more than 20 minutes. Beyond that, the chances of success decrease with each passing minute. If the process ends and the PS3 doesn't boot normally after that, then it is pretty much game over. Your only option at that point is to use the Restore PS3 System option of safe mode, and then restore your data from a backup that you made with the Backup Utility. If no one has been making backups with the Backup Utility, then someone is about to regret that fact. There is no way to recover the data on the hard disk if the Restore File System option does not work, and it often doesn't depending on what the PS3 was doing when it crashed or was powered off. You can still use the Restore PS3 System option to get the PS3 working again, but without a backup the hard disk data is lost.
On the plus side, if it wasn't your job to back up the PS3, then it wasn't any more your fault than it was the rest of your family's. This sort of thing can happen at any time, for any number of reasons. Skyrim on the PS3 is notoriously buggy (it's buggy on all platforms, but the PS3 was the worst). You definitely did not want to run it without installing the latest patches first.
Wait for an hour or two. If it still hasn't started, then it isn't going to work. Turn the PS3 off, and go into safe mode again. Use the Restore PS3 System option. If that doesn't work either, then replace your PS3 hard disk drive.