Thanks for the reply.
Based on the above quotes, I'm pretty sure that I, and (I'm willing to bet) no one can tell what's actually going on with your system. Not even Apple itself! I bet (again) that if you go to an Apple genius bar, they'll tell you to reformat and start anew. Which would be my advice as well.
I may eventually try that, but I'm trying to solve the problem without reformatting first.
GREAT! But, since you're an old-timer, there are some things that have changed in the last 30 years, and I don't mean that in any derogatory way. Back in the 80's PCs were a single-user system, no permissions, no users, no nothing. For example, are you running every day as a simple user or as an administrator? That can make THE difference between a running system and a broken one.
According to advice I've seen in different sources over the years, I have two accounts set up on my computer, one to use to administer the computer as a whole which I created first and almost never use, and one for everyday operations, although I have given both admin rights. Since you mentioned this (and while I was in the process of writing this post), I switched to the other account and tried running VirtualBox there. It ran. Therefore, I must have done something to my everyday account which is different. As you say, I may have to recreate this account to make things work. Let me think and try a few things first, though.
Thanks so much for your help, and if you have any other ideas, please feel free to continue to suggest them!