Well, I figured it out. The first clue was when I pulled the choke out, it didn't feel right: Really loose, like it wasn't connected to anything. I took a look at the throttle linkage and found that the spring had come unhooked and the linkage was all screwed up. I fixed everything the way it's supposed to be and the truck starts right up as always. I have no idea what the weird thing with the starter was, but that's gone, too.
Thanks for the advice.
Joe