27-inch iMac with Retina 5K Display will not complete login

Kenneth Douglas1 wrote:

I started the process for reinstalling macOS Mojave last night, with the option of only reinstalling the OS and keeping the user data. It went through initial process and then went to the login screen. I selected my profile, entered my password, and saw just a small part of the progress bar slowly fill. Then, the computer restarted and went into another phase of the installation process with a white Apple logo on black and a progress bar below it. This morning, it looks like the progress bar has gotten stuck at the same point it was in late last night.

So you’re to the next step, which is the “nuke and pave”; to erase and re-install macOS, and migrate your data.

I suspect bad hardware here.

Kenneth Douglas1 wrote:

I have a Time Machine backup, so I think I'm okay in that regard. You think that reinstalling macOS is necessary?

It’s quite possible this is headed for a fresh install and migration, if this is a corruption and not failing hardware.

Since you have current backups…. Run Diagnostics.

Here are the Apple test tools: Use Apple Diagnostics to test your Mac - Apple Support

Diagnostics might or might not detect transient errors.

Performance problems can be caused by a failing hard disk, or a failing hard disk in a Fusion drive.

See if Safe Mode gets you any further.

Start up your Mac in safe mode - Apple Support

If not, a re-install of macOS might resolve this:

How to reinstall macOS - Apple Support

If not, the next step is an erase and install, and migrating content in from your Time Machine backup.

Erase and reinstall macOS - Apple Support (migrating from TM can be selected at first startup)

Try installing macOS to external storage.

Then migrate your data using Migration Assistant or Setup Assistant.

Here’s an intro to that: Use an external SSD as your startup disk … - Apple Community

This if your internal storage is failing.

Kenneth Douglas1 wrote:

I tried out the Safe Mode option. The post-password progress bar got farther along than usual, but I waited quite a while and it still didn't go to the desktop.

Then you’re headed for a re-install, or an erase-and-install-and-migrate.

I’d probably re-install, and would create an account under a new and different name for the first login, then migrate in all your files and documents under a second and newly-created account name, using the name you want to use. This gets you two login accounts, the first is a backup admin account, the second is the admin account that you want to use. Using a different name for that first login leaves you the opportunity to use the name you want to use for the second login. If the second login fails after migrating in your contents (because your migrated login is somehow messed up), you still have access to the backup admin login.

I'd quick get another External drive to install the OS to to see if we can recover your data.