I downloaded xine and xine-ui again, just to get the freshest stuff. Compiled first time, worked first time. I must be learning how to do this stuff! I also did a “yum update” to get the most recent version of everything, and I upgraded ndiswrapper from .8 to .10.
I moved the computer into another room, and found that I was now getting conflicts on my wireless card. After some research, it appears that I'm picking up my next-door-neighbor's wireless signal as well. I renamed our wireless network, and configured the cards to use only that network, and those conflicts went away.