Ya know - I was thinking of my Brother's Honda sometime after I posted this: it had power to run the lights and accessories, plus it cranked the motor just fine, but it would not fire. Eventually it would fire and run until the cows came home, but the next time you tried to start it there would be a good chance that it wouldn't start again. I was also thinking that when our 850 does fire, it fires right up as though nothing was wrong, so the injectors mustn't be squirting while the coil's not firing, and that got me thinking about the ignition switch.

I'll change it as a matter of course, and we'll keep an eye on it.
Thanks, Marty.