This seemed representative of a Logic Board failure, based on my best guess and some help from idigital, and I was concerned about the difficulty of getting it fixed. After messing with it for 30 minutes or so, I decided to just let it be and go take a nap.
When I woke up 3 hours later, Jess presented me with a computer -- at first I didn't think it was mine, as the battery was no longer duct taped in place (and it was logged into a different user, so the Desktop looked different). Jess pointed to the palmrest pitting and said that it was indeed mine. She had taken it to Organize-It (Still the absolute best store in town for mac repairs) and asked the guy to look at it: he originally said to come get it tomorrow, but 30 minutes later, he had Jess come back and grab it.
At 5:30 on Sunday night, the guy turned around my computer repair in less than an hour: Jess was able to get the machine fixed, literally while I slept.
(The battery that had been loose for a bit was apparently not connecting fully, and therefore had to be replaced as it was causing different voltages or something like that. I'm probably lucky I didn't fry the machine or myself.)
In summary: Jess is wonderful. She took my computer and got it fixed for me. And Tom Roberts of Organize-It is also wonderful, as he fixes things for me in record time. (He even burned me a DVD of "Pirates of the Silicon Valley" -- unfortunately, the last 25 minutes or so of the movie are unplayable, either because my drive is borked, or the disk it's burned on is borked.) It made me a much happier person on Sunday to have my computer back in my hands and working again.