How to get data from a busted iMac hard drive?

I have this same OWC model but like I said the drive does not fit in it becuse it has those plastic pins.

My issue is: when I put it in the Mac Pro running High Sierra, why can't I read the drive?

When I wrote "busted iMac drive" I meant iMac has some hardware issue. The drive is fine, the machine boots, I can get to my desktop but it then shuts down and reboots. It looks like a hardware issue I think.

I just want to access the HD and make a time machine image so when I get a new computer I can migrate from it.

They seem not removable.

And yes, the drive is failing after all, according to DriveDx.

Now, I need to figure out how to get the data back before it does.

I think I will clone it if I can and take it from there.

I put it into an external enclosure but it is the same thing - the system sees the drive but I can't access it. It is not mounted, it can't fix it.

What does "Recover" button in Disk Utilitydo exactly?

The weird thing is that if I put it into the iMac it boots to desktop. It freezes though in a short while and restarts. But it does boot, I see all my files on the desktop.

Doesn't it need the SSSD part to operate? Maybe that's why I cannot access it in another computer?

I don't have another iMac. I have a 2009 Mac Pro and a 2017 Macbook Pro. And the iMac does not want to boot to Recovery. It freezes as well. Weird. Thought it was a MB issue at first.

Where is the SSD part of this drive. Under the MB? I don't see it when the screen is out. And even if I can take it out, how do I make another computer see it as one?

This is my original post explaining the situation:

I really hope someone can help me with this. Thank you in advance.

My mid 2017 iMac's fans have been on high gear for the last few weeks and I decided to clean it. I never did that so I figured that is worth a shot.

I opened it and removed speakers, PS and the HD. I cleaned everything gently with and anti-static brush and blew the dust from under the remaining components with a powerful anti-static blower. There was quite a lot of dust.

I put everything together booted the computer. It started fine and I went on YT, played a video but there was no sound. I took it apart and reconnected the speaker connector to the PS. Put everything together again and the computer froze at login and then rebooted. Next I was able to login to desktop and the same happened. Sometimes I am able to go online but it soon freezes and reboots again.

I took everything apart again and put it together but it did not help.

I am not sure what it is. I ran the Apple Diagnostic Utility (D at startup) but it shows everything is OK.

The only thing that comes to me is the I do not recollect if I disconnected the power cable when I resented that power cable from the speaker. Not saying I forgot to do it, but retracing my steps I think I might have left it on, but of course I did power down the computer. Not sure if it could have caused the problem.

Anyone have an idea what it is. Seems like some MB issue to my thinking. Any way to diagnose it?

Never mind, they are removable. Just found a YT video on that.

Well, let's see if I can hook it up to my Mac Pro with that OWC external enclosure and read it.

Is it possible to recover data from this drive? Not talking about expensive services