I am unable to get my iMac to finish starting up

Start with this...

Safe Boot, (holding Shift key down at startup), does the problem occur in Safe Mode? Could take 10 minutes.

Safe mode attempts to repair Disks & clears lots of caches & loads safe Drivers, & prevents loading of 3rd party extensions, so if Safe Mode works try again in regular boot.

Are you saying you cannot boot to recovery? Command R or use Option on startup and then click on the recovery drive. Is this an intel iMac? Have you tried Nvram reset? Startup with Command Option P R keys down while holding down the power button for two chimes. For SMC shut down and unplug power cord for 15 seconds press the power button plug in the power cord wait 5 seconds and restart.

No screen, nothing?If your Mac starts up to a blank screen - Apple Support

You can get to recovery When in recovery do you see a screen with a box that has Restore from Time machine -Reinstall Mac OS- Safari- Disk Utilities. And down bottom right Continue. And when, lets say, you click on Disk Utilities and then Continue, nothing happens?

If you can get to recovery volume you can run disk utilities to repair the drive.https://www.cleverfiles.com/howto/how-to-fix-a-mac-that-wont-boot.html