My question is how to fix the iMac opening up to screen with progress bar stuck at the end

This may be an indication of a hardware failure. Please follow Apple's steps for troubleshooting in If your Mac won't turn on or start up, if you exhaust all of the steps then the next thing is to contact Apple Support (look in the upper right of this page for a link) and make an appointment to take the computer in to be professionally diagnosed.

Hello, Beanjilly.

Sorry that you're having this trouble with your Mac.

Shut down the Mac by pressing and holding the power button until the computer shuts down.

Then press the power button once again to restart the Mac.

If the Mac still won't start up all the way, then follow the guidance in the Related Article linked at the top or your post and use Disk Utility to repair your startup disk. You'll have to restart the computer in recovery mode to do that.

About macOS Recovery on Intel-based Macs - Apple Support