If the O.S. issue is caused by bad sectors (which it very probably is), trying to fix the O.S. issue will only make the bad sectors issue worse.
This particular HDD model has a particularly bad reputation among data recovery experts. I've had one which failed, and it very quickly went from mild trouble to kompletely kaputt. So if you need files on that drive that are not system files and that are not backed up in some other place than your “backup drive” (which defeats the purpose of what a “backup” should be by the way), do the clone / image now, if you still can. Unless there are only a few files / folders you wish to salvage, in which case it may be wiser to copy those specific files / folders, since there's no guarantee that the cloning / imaging can be completed at this point (that's what I did in the aforementioned situation, and I
ended with only 6 corrupted files, but I knew that these files occupied bad sectors, isolated them while I transfered everything else that was foolishly non-backed-up, and only then tried to get those 6 files, which is when the drive's condition took a bad dive).