Tonight, I got the Windows Media Encoder working, and I was able to get both sound and video from the capture card, so that's configured correctly. It was kind of cool, actually, because I think there's one thing in between that and Peercast that will need to be done for me to start transmitting.
Now, of course, the bad news (which, granted, isn't so much bad as it was frustrating, but hopefully easily fixed).
I can't seem to get that Cyberhome DVD player (the one that plays everything, including TDK discs, which apparently NO other DVD player likes to play) to loop the whole disc. Fortunately, there's a Sony DVD player sitting upstairs being unused at the present time (long story). It doesn't matter, though, because with any luck, this will be temporary.