holdent, you called it. Thank you. It's fixed now.
The long version. (reason for the delay: I decided not to tackle this until after I returned from a trip.) Anyway, tried removing the battery for a couple minutes, but that didn't work. So, I called Logitech support which was, as reported, excellent. It turns out that a factory reset was all that was needed, and everything is up and running smoothly. I thought that I had tried the factory reset by selecting it from the menu when it first happened, but maybe I did something wrong. Instead, the service person told me to press the + and the "home" key at the same time at turn on to force a factory reset. It found my network right after that.
It's bizarre that it stopped working in the first place, but bonus points to Logitech for walking me through it.