So, I did what any single girl who has no idea about furnaces would do: Googled a repair company. There was one right down the street! He came, he looked, and he said, "Hope you don't need heat tonight."
Good thing I have that fireplace. It's much more useful than just being cozy watching movies.
Long story short--okay, it's a short story--is that I need a new part. He's going to come back and fix it tomorrow. I have no idea what it will cost, but my guesstimate is somewhere around $200. It could be a lot worse. Let's hope that it's not!