The answer, as it turns out, was the laptop power cord. I noticed there was some damage to it yesterday, it looked really worn and I went looking for electrical tape to strengthen it, unfortunately we didn't have any in the house.
So this afternoon, I pulled it up and it looked like this:
The burn and the protruding copper wires are new as of today. Needless to say, I won't be using that anymore.
What really gets me about this isn't the fact that it broke: I haven't been taking good loving care of it, though neither have I really put it through the wringer, either. Also, I have the money to afford a new one, though I still think they are too expensive.
What really got me was when I started reading the comments that people had left on Apple's site about the product. Apparently similar kinds of failure in a similar spot is a very common problem, and I was in fact lucky that my cord made it more than a year. That's disheartening, because they should have fixed it by now. I wasn't terribly happy with the design anyway (it has a big weight on it that stretches the cord, and I've been worried about how hot the cord gets), but this takes the cake.
Unfortunately, I don't really have a recourse:I just had this computer repaired a few months ago, and I can't exactly use it without a power cord. Hopefully I'll be able to mooch off of a roommate's until my new one arrives, but it's also possible I just won't be online as much. Bo-urns.