Thanks for your suggestion. I tried what you suggested but it didn't work.
Let's try a 2nd version of the experiment Slydude suggested.
1. Power everything down (both the computer & the external drive).
2. After powering everything down…disconnect the external drive from the computer.
3. Now do an SMC Reset on the computer:
https://support.apple.com/en-us/HT201295
Skip down to the part which says…
"If you're using a Mac notebook computer…"
4. Restart the computer as indicated in the SMC Reset procedure.
5. Now Shut Down the computer.
6. If the external HD has it's own power switch or power cord…now plug it into the power and/or flip the power switch.
7. Plug the external HD's cable (USB cable I assume) into the computer. If the external HD has only one cord (a USB cable)…plug it into the computer.
8. Start up the computer.
9. Try the Disk Utility task you were doing previously.
One word of caution (which Slydude wisely referred to). Never unplug an external hard drive from the computer while everything is powered on…unless the external HD was properly ejected first (drag the external HD's icon to the trash can). If this is not done…directory files can get damaged…possibly leading to the problems being experienced now.
- Nick