The only way that I know to disable a soundcard (I'm using Win XP). Is to click on Start and then select Control Panel. From there scroll down the list and click on System, then select the Hardware tab and click on Device Manager. Select Sound, video and game controllers, right click on your soundcard (in my case it's Creative SB Live! series and select disable. You will see that it now has a red x next to the name to tell you that it is disabled. You can now run Pirates to see if you can get past the spinning wheel screen. If you can, you know for sure it's either your soundcard settings or your drivers for your soundcard need updating. When you're ready to re-enable your soundcard return to the Device Manager screen, right click on your soundcard and select enable. Your soundcard should now be functioning fine.
As with DXDiag, this does carry some risk (as does nearly every Windows operation) so this is done entirely at your own risk.
If the game still doesn't work, I suggest trying the Atari Help Forums (and make a search for spinning) and hopefully someone can help you there. You can find the forums here;
http://www.ataricommunity.com/forums/index.php?
Good Luck.