Mac will not boot up

Thank you for the quick response. I’ve tried your recommendation, but unfortunately that did not work as the system shut down after exit. Tried a normal boot next and got the same result..

Next, I rebooted in Command+R mode, Disk Utility only to see the same capacity (999.35 GB), though it sounded like trash was being deleted when I tried those steps.

Strange, now it won’t even boot up to Disk Utility (Command+R), I let go of the command after the Apple logo appears and about 15-20 seconds later it shuts down. So now I can’t even reinstall OS X. Any other suggestions, or is this a lost cause?

BTW, if it is a lost cause, I’m wondering if this may be the only potential last resort option: connect the device to my other good Mac, then reboot the bad Mac and immediately press T? Supposedly this will give my good Mac Access to the hard drive on the bad Mac just as if it were an external hard drive, so I can at least copy over important files. Do you know if that’s possible?

I have tried PRAM reset and then the SMC reset without success. Even tried them several times.

I still can’t get it to boot up to the Utility Disk anymore either. I do have OS Catalina installed on an external drive 1.5TB drive, is there a command I can use at start up to get it to automatically boot up the external drive without going to Utility Disk?

The command worked, but still could not boot up the computer from the external drive as it would still shut down.

So, each of these approaches fail as the computer continues to shut down:

1) Normal boot up or Turn-on;

2) Turn-on, Command+R;

3) Turn-on, Option;

4) PRAM & SMC reset

I do not recall the exact model year of this Mac, but it’s at least 10 yrs. old. Perhaps the auto-update that occurred that seemed to start this whole problem is not compatible with the hardware?