I was going to buy a new one, but decided to try and fix it. I just had to replace a $7 capacitor, and it worked! I might still replace it anyway (maybe next year), since I hate the hum of AC fans.
Indeed they are! Obviously they have their own power supply to convert to DC, so they connect in a similar manner as a standard AC fan. They are a lot quieter, and usually let you have more speed settings.
Thanks! It's actually difficult to find AC fans nowadays. Most are DC. It annoys me because I have separate light and fan switches on my walls, and that doesn't work with DC fans.