EDIT: Solution found. Mac inherited a Linux terminal tool called fsck, which does disk repairs. I booted up the Mac into Single User mode by holding Command-S, and then ran

fsck -fy /dev/disk0s4

where disk0s4 was the name of the broken partition according to Disk Utility.

That program finished the repair in under 5 seconds for me and it was a success!

My refurbished (two week old) Macbook Pro 2015 15" Yosemite has two partitions, one of which is in exFat format. Randomly today I went to open up a project on that partition, only to find it was not visible in Finder. I used Disk Utility and saw it was greyed out and named "disk0s4" instead of Shared like it was originally named when created.

Debug mode Disk Utility's "Verify Disk" responds with

Invalid sector size: 0

File system check exit code is 8.

Error: This disk needs to be repaired. Click Repair Disk.

When I then click Repair Disk, it replies with

Disk Utility stopped repairing “disk0s4”

Disk Utility can’t repair this disk. Back up as many of your files as possible, reformat the disk, and restore your backed-up files.

I waited a bit and then tried again, hoping it was just a fluke, only to get this different error message

Invalid sector size: 0

File system check exit code is 8.

Updating boot support partitions for the volume as required.

Error: Disk Utility can’t repair this disk. Back up as many of your files as possible, reformat the disk, and restore your backed-up files.

I'm not sure how to (or if you can) back up files off of a disk I can't read. I don't have any backups of it... I just got this Mac two weeks ago and moved all those files from my Windows PC. I sold the Windows PC so the other copy of those files are now gone.

Is there any way to solve this?

Thank you so much for your time