Installing Monterey & can't re-start. Only Apple Logo and progress bar.

To cover all your bases, you might want to reach out to Apple Support over the phone and have them guide you. That's what I did, and the incredibly helpful 'senior advisor' had me do this:

Start in 'Safe Mode', erase the disk using 'Disk Utility' and then use 'Internet Recovery'. This got me to 'Sierra' since that's what I had originally. (I tried to reinstall High Sierra, and it wouldn't work) From there you decide which OS you want to install (I went with Monterey found in the 'App Store'). After installing it, and starting it successfully with a temporary ID (don't try to recover any files yet) -then restart the computer in 'Safe Mode' again. If you have the option to re-install the updated OS you just installed -that's good. Still in Safe Mode, erase the disk again. Then reinstall the OS again. After that, when the updated OS starts from scratch -use 'Migration Assistant' to recover everything from 'Time Machine'. Sounds like a lot of repeating, but it did the trick for me. Good luck.

As a favour, since I generally do not take on two different uses on the same question exception is the OP posting.

There are reports appearing on the Apple Support Communities ( ASC ) Forums regarding failed installation of Monterey on older Qualifying Apple Computers. In most cases this is related to having a NON Apple Original internal drive ?  

The EFI Boot ROM included in Monterey is verifying for Original Apple Drive and if not found , may Balk or fail to upgrade to Monterey. 

Reports indicate the EFI BOOT ROM is Required to Flash the Computer and is a  requirement for a Successful Monterey Installation.

If this computer has an After Market Drive - the solution is the swap out the After Market Drive for an Original Drive. The run the Monterey Installer to the computer. Then reverse this procedure and run the Monterey Install onto the After Market Drive.

Empty Space Requirements specifically for Monterey  >> If upgrading from macOS Sierra or later, your Mac needs 26GB of available storage to upgrade. If upgrading from an earlier release, your Mac needs up to 44GB of available storage. 

Suggest restarting in Safe Mode. This will perform a Disk Repair, clear cache files and only load Apple Software, extensions and fonts. The boot up will be slow and can take some time - Normal.

This may or may not allow the UpGrade process to complete

Fusion Drive ?

After Market Drive ?

Any Third Party Applications that will interfere with the normal operation of the OS, alter, modify, remove or delete or attempt to do so is an invitation for disaster and may require a Reinstallation of the OS.

Any of the below may interfere with the Installation process.

This includes AntiVirus, Disk Cleaners, Disk Optimizes, UnInstaller etc.

Any of the below should be removed as per Developers Instructions 

This will include CleanMyMac , This will include BitDefender , 

This will included Norton Antivirus , Sophos Av Software

Intego AntiVirus, McAfee, MacKeeper, Avast AntiVirus

Ad Guard, Webroot

The The Built in Security  is all that is required.

I followed the steps listed (iMAC late 2015) started is Safe Mode (twice) and have the ‘macOS could not be installed in your computer’. Are you now telling me I have to erase my hard drive? All of this because I wanted to update my computer? Seriously?

Thanks for the help.

It’s the original intel processor that came with my iMac 21.5” late 2015 model. I have over 100GBs of free space.

Thanks for the assistance. That’s a lot of info but it doesn’t help me at the moment.

I reached out to @AppleSupport on Twitter and they have me trying ‘Internet Recovery’. Fingers crossed.