Thanks everyone for the responses. I haven't had a chance to work on it yet, I will this weekend. Just a few comments based on the responses:
- When I started the car to leave home, I thought to myself something sounded a little different, but I woudn't be able to describe what was different now.
- I was sitting at a light, the light turned green, and I started to take off. I started moving, and the car died with a last dying breath kind of thing ....Pluuuuuh. (Ignition control module died? When it happened in the past though it was a very calm death, with the engine just kind of stopping with no real noise. Could be because I kind of punched it hard because I hadn't noticed the light turned???)
- I coasted a couple hundred feet and stopped the car.
- I tried to restart it
- It seemed to turn over fine and sound like a normal car trying to start but you knew wasn't going to. I probably tried to start it less than 10 seconds.
- After a brief rest, I tried to start it again, and the starter was definitely going slower, and stopped completely after maybe 5 seconds.
- I swapped in my spare Ignition control module, tried to restart, no response from the starter. At this point I saw some smoke rolling out from under the hood, and went to check. The insulation was getting soft and smoking on the cables from the battery to the solenoid, and from the solenoid to the battery. I also noticed a small pool of molten stuff on the ground below the starter.
- I disconnected the battery, and let things cool off. After 20 minutes or so, I reconnected the negative cable to the battery, nothing adverse happened.
- The flashers worked the entire 2 hours while I was waiting for the tow truck, so the battery seemed to be in good shape.
- I didn't hear any other strange noises, like the starter grinding against the flex plate, or the starter staying engaged after I got the car started.
- The starter and ignition control module are less than 6 months old.
I'll start with the solenoid and the starter, and see how far I get.
Thanks again for all your comments!