The defrost timer was probably ok. I had a repairman come out and the problem was the startpak/relay/overload. This is a small device located next to the compressor. It's a fairly common problem. To tell if this is the problem, the compressor was very hot but it would not start (due to this defective device). Without the compressor starting, of course, the refrigerator and freezer did not cool at all. The defrost timer, if that was defective, as I understand it, the little fan in the freezer would not run. But it did (periodically), which meant that the problem was this startpak.
The defrost timer, as I understand it, is a fairly common problem as well.
Rich, thanks for your help.