Today I finished my first foray into home appliance repair! Apparently, the most common point of failure by far for rice cookers is the thermal fuse, which seems to be hidden along some wire inside the cooker.
I found mine in a piece of plastic shielding near the edge of the casing, presumably where the 142 degree tripping temperature would indicate a serious problem and stop the machine from seeing things on fire. Thankfully, a YouTube video had all the answers, and, having located the little device, it was a simple matter to get another from my local radio shack and replace it tonight. Now I'm watching its lights flow again, and it's starting to steam. So, as long as it doesn't catch fire, I think I can count my first repair a success.
It's empowering to be able to fix the machines that work for you. I find myself hoping that something else fails soon so I can learn how to fix something else as well!