Did you check out the tech support walkthrough? Privateer does not work in straight Windows at all. You must use something like DOSBox. If you have an older/slower computer, then you need to reboot in DOS mode with all the appropriate drivers and such set up (these days it's much easier to get going on a modern Windows XP/Vista computer in DOSBox).
I installed it in DOS, and then when it was done installing, I rebooted in DOS and started it from there. As far as the drivers, i checked my sound card for DOS settings and put those in at the beginning of the installation.
Are the DOS drivers for the sound card being loaded when you reboot in DOS mode? Do you have a config.sys and autoexec.bat? Try reinstalling the game and selecting no soundcard. If the game starts up then, you'll have at least narrowed down the problem there.
Are you specifically trying to play this on an old computer? Do you have a newer machine to run this game on?