Well, crap...I feel pretty foolish.

Turns out the negative battery clamp (the thin brass one) was pretty crusty inside with hard, corroded oxide (heh, rhymed)...I just went out and cleaned them both (the positive just needed a little brushing), and now it fires right up.

I've just never seen crusty terminals cause this sort of behavior...it's always looked like a dying battery, with dimming lights and stuff, but not a hard kill of everything electrical.

Harrumph.