1. Purchase a copy of Disk Warrior and run it against the drive.
2. Replace the drive, put the original in a case and salvage what you can.
3. When complete, get yourself an external drive, other than the one you already have, and use it for Time Machine.

Given this built-in, automatic, function of the OS, I can never figure out why someone does not have a backup.

Remember, we only lose what we fail to backup.

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