Argh, I don't check the forum for two weeks and I miss the one question that was totally designed for me.
Indeed, this figure is Saki Nijino, one of the dateable girls in the mid-1990s Konami dating-sim game Tokimeki Memorial, which was released on multiple consoles of the era. The game covers the three years of the protagonist's high-school experience, hopefully ending with a declaration of love from one of a dozen girls beneath the cherry blossoms of the school's giant mystical tree. (Or something like that.) The game itself is primarily focused on choosing activities to modify various parameters, for which the various girls each have certain preferences (Saki likes guys with high athletics and perseverance scores), and befriending and dating these girls.
Saki herself is a sweet and positive girl, preparing bento lunch for the protagonist on one occasion, and she's manager of the school's soccer or baseball team (depending on which of these you join, if I remember correctly, that's the one she's manager of). She's the only girl I've actually successfully finished the game with, which may be part of the reason I have a soft spot for her. She's also one of the girls who frequently appeared in promotional material; while Shiori, the red-haired childhood friend, was unquestionably the "mascot" of the series, Saki, Ayako (the artist who peppers her speech with English words and phrases) and Miharu (the mysterious koala-loving girl with green hair braided in loops) also were prominently promoted in posters, figures and pencil boxes and the like.
I have a few figures of her, though the one you have isn't one of them.
This is a 1/5th scale soft vinyl figure by Kaiyodo. It's the largest figure I have, not counting dolls. She's wearing her winter uniform here.
And here's a recently released (2010) 15th-anniversary figure that was intended for UFO catchers (crane games). She's wearing her summer uniform here.
And the winter and summer versions of her smaller blister-packed action figure.
As for your Saki's missing hand, I'm wondering if a spare Obitsu hand might be a potential replacement, with a bit of modding. As for how she ended up in a thrift store in Nowheresville, Alabama... well, it's not entirely far-fetched, as I'm a former obsessive TokiMemo collector from Nowheresville, Maine. It'd be interesting to know how she got there, but it will forever be a mystery, I guess. At least now her identity is not.
