Q: unable to backup to Time Machine

The Backup disk image ... sparsebundle ... is already in use.

You might try clicking on that link before posting a reply.

There are three sparse bundles on the backup drive. One for each computer that backs up to the same drive using Time Machine. You need to apply repairs to the proper one. Are you doing that?

This is not something I do, although I've done this once or twice in the early days of Time Machine. So here's what I remember:

Simple solution (from Bob Timmons):

Now I also seem to recall mounting the "bad" sparse bundle by double-clicking on it. Once mounted it will appear as an ordinary disk. Use Disk Utility to repair the disk (do not repair permissions.) Then eject the mounted image and see if you can once again use it.

If this is all a big failure, then I think you are left with using Time Machine to place that particular computer's disk into the Exclude list. This should delete it so you can start the backup from scratch.