Re: So long...
"Her little Win7 box, custom-built on a budget about 5 years back and running almost bugger-all aside from Chrome and a few lightweight hidden-object games, was running slow and spitting low-disk-space errors."
Xubuntu LTS with xfce4-popup-whiskermenu bound to mod4 and the panel unlocked, dragged to bottom, and locked again. Chrome installs fine. Looks like Win7 ish - my students can use it on my old laptop without further instruction. Would run fine on hardware suggested above.
I'm not sure about the hidden object games but there are plenty of desktop games available.
Or then why not a Chromebook with a minimal account set up?