That was when Gretchen brought to my attention a persistent error message that she'd been getting on the machine. It turns out that the flash storage on this machine is so small that it has become impossible to install the latest Windows 10 updates directly.
I have cleaned off everything that I can remove from the storage. This brought the free space up to 3 GB, which is still not enough to install a Windows update.
I now have the updates installing (maybe!) by grabbing the now-empty 32 GB SD card from Gretchen's dead camera, plugging it into a card reader, and using that as an auxiliary drive. There is a word for this procedure: insane.
My understanding is that the effective maximum configuration for these machines is prescribed by Microsoft, in the sense that anything more robust has to pay a much higher fee for a Windows license. So HP has built a machine to Microsoft's specification that cannot actually run Windows in a reasonable fashion, given that you have to believe that installing the damned updates is a vital function of Windows.
Somebody here needs to get their act together.