If your harddrive is broken, the PS3 will just keep complaining and potentially make things worse, which is why I recommended
not using the PS3's backup function. It's a shame now you've lost your old backup.
Just copying your saves and any media off the disk might be fine, but there is always the chance of corruption (admittedly, this is true of making an image, too) - that is, it might be fine on the disk, but depending on the nature of the fault, it might be possible that as the file is copied ("backed up") it
becomes corrupted. This is the risk you face. You might get lucky after multiple attempts, depending on what exactly is wrong.
But: you cannot just copy
all the files from the PS3, format the drive, replace the files and expect it to work. There's issues with file system etc., again why I suggested the image method (since it preserves all the low-level formatting, invisible in most file systems).
I'll try to break it down, if it seems a little unhelpful so far:
- Limit all activity on the corrupt hard-drive to the minimum operations - any and all access (read / write) could lead to further corruption, depending on the fault.
- Back up:
- Either copy the minimum files (saves etc., as in the post above) from the PS3's drive to storage
- Or make an image of the PS3's drive by connecting it to your PC and using an image making (or "cloning") tool and save it somewhere on your PC, or external storage.
- Format (a preferably new, or at least a different) HDD for the PS3 - test it's working fine (install a game, do all the things that reported corruption before etc.) - if you still get errors, and you're certain the new disk is fine, then the PS3 could be at fault (unlikely).
- If all is well, restore the backup to the new HDD.
- If you just backed your save files up, this should be a simple copy (assuming users match, I'm not sure on that though - others probably will know more.)
- If you imaged the old drive, connect the new drive to your PC and write the image to the new drive (using an image / cloning) tool and test it in the PS3. There might be some corruption that needs fixing, which the PS3 might be able to do by itself. A suite of disk repair tools (like Seatools) could help here, too.
To be honest with you, I'm leaning towards just copying your saves and sticking a new drive in the PS3. If you need anything else, keep the old disk just in case.
Whatever you do, be sure to plan each step and make sure you know you're not going to lose data you need (i.e. data you don't have anywhere else and can't get hold of again.) Welcome to computers, by the way.
Finally, Good Luck. 👍