I mail-ordered a new water pump. Got it the other day, and installed it today.
I've never done one of these before, but I just followed the directions, removed the old gasket, cleaned it all, put the new gasket on with some tacky goo, and bolted it all back together.
Nice and shiny!
Normally, the fan blades would mount right on the water pump, but I think I will probably convert it to an electric fan anyways.