2008 iMac stuck on loading screen, cannot boot or backup files

It sounds like the internal Hard Drive may be failing. What you describe are classic symptoms for a failing Hard Drive and it would not be surprising for a 2008 model. If I am correct, then the more you attempt to "fix" the system, the more likely you are making the drive failure worse where even an expensive professional data recovery service will be unable to recover any data from it.

It is possible to attempt to boot from a bootable Linux USB stick and check the health of the physical internal Hard Drive. I can provide instructions if you are interested.

Have you tried booting from the gray disc that came with the Early 2008 iMac by pressing and holding the C or Option key and then use that Disk Utility on the internal boot drive? If you got that far, is the internal drive full, which would block successful booting?

"Unfortunately it’s not even loading to the log in screen. When I used yesterday morning I was able to log in and use with no issue. Now it’s stuck on the Apple logo with a bar beneath it turns off halfway through loading"

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Go Here: If your Mac Starts Up to an Apple Logo or Progress Bar - Apple Support

"I can’t enter safe mode but I can enter recovery mode should I do it there? When I unmount (all are mounted) what shall I do next?"

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Mount the Drive and ALL Volumes:

Yes. Use "Recovery Mode". Unmount and then mount is what to do for any drive and volume already mounted. Just mount it, if it reads "Unmounted".

1. Boot: in Recovery Mode
2. Select: Disk Utility
3. Select: each drive and each volume
4. Select: Unmount
5. Select: Mount
6. Restart your Mac.

"Unfortunately it’s not even loading to the log in screen. When I used yesterday morning I was able to log in and use with no issue. Now it’s stuck on the Apple logo with a bar beneath it turns off halfway through loading"

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Mount the Drive and ALL Volumes:

You Mac need to have the hard drive and all volumes mounted. So, while in Disk Utility, mount ALL unmounted drives and volumes. If already mounted: unmount them(if already mounted), and then Mount them. Perform this one volume as you work your way down. The Mount button and Unmount button is located to the top-right corner of the window.

1. Boot: in Safe Mode
2. Go to: Select Disk Utility
3. Select: each drive and and each volume
4. Select: Unmount
5. Select: Mount

"2008 iMac stuck on loading screen, cannot boot or backup files: [...]Is there any other options left? It was working fine yesterday until I restarted. I hear no clicking noise either that would indicated a failed drive. All I want is to turn it on so I can back up files onto an external drive."

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Try Resetting your Mac Login Password:

Reset it using the login screen. You'd go through your Apple ID to perform this. Find out more here: If you Forgot your Mac Login Password - Apple Support. Make sure that caps lock is not enabled when typing it.  Does that fix this?

Wait it Out:

If you haven't touched this for some time, then it may need to get with itself.

"2008 iMac stuck on loading screen, cannot boot or backup files: [...]Is there any other options left? It was working fine yesterday until I restarted. I hear no clicking noise either that would indicated a failed drive. All I want is to turn it on so I can back up files onto an external drive."

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Other way the Reset the Password:

1. Boot: in Safe Mode
2. Go to: Select Disk Utility
3. Select: Utility menu
4. Open: Terminal
5. Use: this code:

resetpassword

“I unmounted Macintosh HD and now it’s letting me mount.. should I restart?”

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Mount, and then restart.