2015 iMac running Mojave hangs on Start up

Agreed. It’s weird that I get different behaviors with command-R and command-option-R beyond being offered different systems to install. Since otherwise the pages look the very much the same. But command-option-R asks for the WiFi (as expected) and then goes through a routine with a spinning globe before the Apple logo and progress bar comes up. Whereas command-R goes straight to logo and progress bar. Command option R yields a wifi indicator in the bar at the top, allowing me to choose wifi there as well. So peculiar. New system is installing. I’ll report back in four hours or so when the system is done installing as to whether the computer uses self now boots all the way.

So I was able to create a bootable external drive and start up from that. I'm still getting some odd behavior, including the Finder raising the ball of confusion for an extended period of time that required a restart. But I can now work from the machine. I can rescue a few bits that hadn't been properly backed up (since I mostly store this machine's documents in the cloud, the need for a Time Machine backup hadn't seemed pressing).

If I now make a Time Machine backup of the old system drive while running under the bootable external drive, will that allow me to restore all my various settings like a regular Time Machine back up if I use that back up to restore or does that only work when you run the Time Machine when the disk is the system disk? Or is it best just to nuke it with a reformat, reinstall the system and then move what I need back on it by hand, like a clean reinstall?

I’ve tried safe boot and command-R. Command-R doesn’t ask for wifi access and there’s no way to connect to the internet remotely. I haven’t yet tried connecting the computer to the internet with Ethernet.

Now, I'm presented with where to install the system, and I'm given two potential disks, data and update. I presume the latter was created when the first installation failed. But which do I want to select for this? If I ever get this computer to reboot, it seems like I'll need to spend a lot of time restoring...

ok, now I have a new problem. I can't seem to get the migration assistant to read my old settings. It will read the new "Update" drive but not the Macintosh HD - Data drive. And the latter has all the settings and apps, whereas the former seems to have been the attempt to upgrade it to Monterey, the last system that this machine supports. Any idea how to migrate the settings? Also if I want to try installing Mojave again on that internal hard drive, is there a way to do that with you formatting it. I plan to do that soon, but there's still some clean up I'd like to do if it's possible to make that drive bootable again so I can access my old account..

I ran diagnostics. it reported no problem found. But it did connect to internet to run the diagnostic. So I suppose that rules out the WiFi card.

Option-command-R did ask for the WiFi. It means updating the system, which I didn’t want to do, but if it can get me to boot into the system that’s certainly an improvement!

So, Installation of new system failed for unspecified reasons. Apple error messages are really not helpful on this. Now trying to boot/reinstall from bootable installer.