Okay, I figured it out. I think that sometime ago, I had installed a codec pack (prob Klite or something like that) and uninstalled it since. Between that and who knows... my system no longer was configure to play WAV files.
I could play WAV files in the c:\windows\media folder, but the ones in the C:\Program Files\GOG.com\Independence War 2 - Edge of Chaos\streams\audio\speech
would not play any sound.
When I tried to bring them up in Windows Media Player, I got a dialogue box complaining about needing a codec to play them, although they DID play in winamp.
After a bit of searching, I found this posting --
http://www.moviecodec.com/audio-codecs/need-codec-0x0022-37173/
The gist of it was that the codecs I was "missing" should be in the windows system32 folder, and have an .ACM extension. The should be refered to in the registry under HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows NT\CurrentVersion\Drivers32
I checked this registry location, and sure enough, the entries did not match that of another XP machine that I was using to compare. Also, I found that I HAD the ACM files in my system32 folder.
After adding a few entries to my registry, I can now hear "Jefferson Clay" just fine.