What you are describing is exactly what was happening to me. It turns out it was an update that didn't complete and by deleting the contents in the Software Distribution folder did the trick.
Thanks for the help, and confirming it was the same symptoms, Craig. I copied the Software Distribution folder onto the desktop, then deleted the contents of the original. I then went through the re-installation process, and that went OK. I rebooted and was looking forward to the computer shutting down OK, but sadly, the app message is still there when shutting down. I have just had a message that a Dell update is available, so I will get back if that has made any difference. but I can't see that helping.