To be fair to Apple, I finally found the problem. Apparently, the silence button is easily moved to the silence position because I never use it (I just turn the volume all the way down) but it in fact was the source of the problem this time. In fact, it happened again to me today. Too bad there isn't some visual indication that the phone is silenced.
I was frustrated with Apple because I did a software update last year to our iMac and it would then randomly freeze to where only a hard shutdown would work. Many other people were having the same issue. Apple never acknowledged the issue but after some number of months, the computer started working normally again.