Late 2010 iMac getting quarter way in booting then turning off Late 2010 iMac getting quarter way through booting then turning off

Ok - first things first, apologies for a long post - I have lots of details about this issue.

Context:

As far as I can remember, about a couple of weeks ago I was working on my iMac (Late 2010, I believe running High Sierra) and it got stuck and froze (the spinning rainbow wheel of doom).
I waited for about 5 minutes then force shut down the iMac using the Power button. From there, the iMac simply refused to start up. It would get halfway through a very slow boot up - i.e. loading bar gets halfway - then simply turn off and die.
Here is what I have tried, and the various results for each:

My attempts:


Safe Mode - I attempted to boot into Safe Mode by holding  shift  when I turned the computer on. Unfortunately it simply doesn't get to Safe Mode, the iMac turns off half way.

Recovery Mode - I attempted to boot into Recovery Mode by holding  Cmd  +  R and succeeded, but when I attempted to perform first-aid on the drive, I got this:




Booting into a different drive - I only have the recovery drive separate, so same result as (2).

Performed Apple Diagnostics (on my iMac known as Apple Hardware Test) by holding  D  on startup. I ended up with error code -3403D.

Reset NVRAM multiple times by pressing Option  + Cmd  + P  +  R - no change.

Reset SMC multiple times by unplugging. No change.

Booted into Verbose Mode - everything went smoothly until it got to checking the Catalog File, where it stopped, before spewing an error message and shutting down after 3 seconds.

Booted into Single Boot Mode by holding  Cmd + S on startup and typing fsck -fy. I repeated this over and over but it didn't say anything different, just that the drive couldn't be verified completely.



Question:


I'm aware there may be ways to fix this by reinstalling MacOS. I'm also aware that this could be a hard drive issue, however, I'd like to exhaust all other options before I consider that. Are there any other ways anybody knows hot to fix this?


Note:

I'd like to note that now, a few weeks after the initial issue the iMac only makes it quarter way through the boot before turning off.
I'd also like to note that I have seen these websites:
https://www.stellarinfo.com/blog/solved-macbook-pro-booting-stuck-halfway/
https://discussions.apple.com/thread/8464773
https://discussions.apple.com/thread/8381789
https://discussions.apple.com/thread/7051661
https://www.ifixit.com/Answers/View/218110/Why+does+my+iMac+shutdown+halfway+through+loading+on+startup
iMac gets stuck halfway through boot
But nothing has worked. Can the Apple Stack Exchange Community help me better?

Thanks!
I've seen this issue quite a few times before. For me, I booted into Single Boot Mode by holding Cmd + S on startup and typing fsck -fy. Let that process run and keep repeating it over and over until it says the volume is ok.