It turns out you can replace your video card fan. The downside is that it's fiddly, nervous-making work. I saved about a hundred dollars over replacing it. Not sure what it would have cost to get it repaired at Fry's or Best Buy, but I'm glad I didn't find out.
And what's up with RAM heat sinks on video cards? Do they actually do something, or is it just feature-itis? Well I installed them anyway, sigh.
The silence that came out of my PC case last night was music to my ears. I feel better already.