Arkose: Do you see any error messages when you run DOSBox.exe directly? By default this is in:
C:\GOG Games\Wing Commander Privateer\DOSBOX
Running DOSBox directly shows an additional Status Window; if the problem is specific to how DOSBox is accessing the sound it will show something about it there.
If DOSBox doesn't show an error the cause is something else. Possibilities include the game running in an antivirus sandbox (as in Avast! and some other products) or DOSBox being muted in Windows' Volume Mixer.
No errors when I run DOSBox, but after installing AC3Filter, the voices and ship sound effects work. Music and all other sounds are silent, even though music's switched on.
I tried reinstalling, same issues. I shut my antivirus off while playing and installing, same issues. I'm running on XP, and as far as I can tell, there's no issues with volume control.