Can anyone advise what to do when my iMac stalls while booting on the black screen ? I see the white progress bar about 3/4 through and then the computer shuts off. Any insight is greatly appreciated.

At this point in the boot up process, your Mac is attempting to load kernel extensions. Think of them as device drivers.

I suggest trying steps 3-6 in the following article to see if they can help:

• Mac Basic Startup Troubleshooting Steps - Apple Community

Please post back your results.

Okay, its useful to know that you could start in recovery mode. You should run Disk Utility first and then click on First Aid - that's the disk repair program. If it reports no problems, or if it reports problems found by fixed, you aren't done yet. If it reports problems were found and not fixed, we'll need to have another talk about what to do next if you don't have a current TimeMachine backup. If you do, select the restore from TM option.

Disk First Aid repairs file issues but it's almost certainly not fixed the problem that caused the crash. You'll have to do 1 of 2 things next. 1) download the operating system and reinstall it or 2) use your TimeMachine backup to complete restore the hard drive. If you've been keeping up to date with your TM backup this is probably the better option.