my mac won't start up after os update from big sur to monterey

Try Shutting down by any means including the Power Button. Disconnect all external drives. Restart and immediately hold the SHIFT key until the Apple Logo appear, then release.

Safe Mode may or may not allow the upgrade process to complete.

What year iMac?

If you have the 2017 iMac Pro or the 2020 iMac the you may have to use another Mac and use the method discussed here:

Revive or restore an Intel-based Mac using Apple Configurator 2 - Apple Support (CA)

If you have access to another Mac that can run Monterey I wood create a bootable USB install media w/Monterey and then boot from that, erase your current startup disk and then install Monterey and migrate/copey necessary files from your backup to your new Monterey install.

Apple’s instructions

How to create a bootable installer for macOS

So none of the screens shown in the support article appear? Just a black screen? If that is correct, does there appear to be any illumination around the edges of the screen? Do you hear anything running inside the Mac?

I am assuming that you have an Intel-equipped, not an M1 iMac ... correct?

Starting in Safe Mode does the following.

It does a Repair Disk, clear cache files and Eliminates all Third Party software, extensions and fonts from Loading.

It also loads minimal Native Apple extension and processes.

No harm to the computer or operating system

What exactly do you see when your Mac is failing to start up?

Ref: If your Mac doesn't start up all the way - Apple Support

I get this error message. can’t move forward and won’t start up

A critical software update is required for your Mac, but an error was encountered while installing this update.

Your Mac can't be used until this update is installed

Hi P.Phillips,

I may try this suggestion, but first does this action cause any other problems…

I am stuck at the screen which shows the apple logo and the line with the update progress.

I had restarted my mac after installing software P-Touch Editor 5.0 to use with a Brother label maker.

Thanks

thanks. Tried and failed.

it just would not push past the select wifi screen. Went out and bought a new one. Mine was a 2017 MacBook Pro.