I was convinced this was a software problem and apparently it was. I tried pulling sticks of RAM, leaving the case open for cooling, etc., and nothing helped. Finally, by trial and error, I found that the "Dell Control Utility" that was installed with my "Dell Truemobile Wireless Networking" software was at fault. When it was deleted, everything was back to normal. Curiously enough, the wireless network continues to work fine. (The affected computer was a desktop connected to the WAP by a Ethernet card/cable.)

Whew!