How I did it
In case anyone in the future ever cares, this is how I did it: I downloaded Audacity (1.2.4), and it only allows you to import audio files. You have to first demux it somewhere else, which was all I needed to do anyway.
I downloaded Windows Media Encoder 9, which includes Windows Media Stream Editor. I converted my video clip to WMV, then used the Stream Editor to grab just the audio. It worked perfectly the first time.
P.S. Didn't try Virtual Dub - that might work, don't know.