It's Alive! It's Aliiiiive!
OK, one new battery and a lot of money I don't have later, and my car works again. Unfortunately, it's now making a loud whining noise that sounds like the timing belt is out of alignment. When I first bought the car the timing belt snapped in the first week, so this one is only 6 months and maybe 5,ooo miles old. I'm just crossing my fingers that it won't need replacing. I probably need a second job.