The game has some problems when it comes to the sound. It's looking for a microphone, and if it doesn't find one, everything dies. Of course, a simple solution is to plug in a physical mic, but if you're like me and playing on a HD TV and your PC doesn't have anything but HDMI ports, you don't have that option without some special cables and such.
But if you're thinking about asking for a refund and returning the game, don't! The solution is simpler than you might think!

You really only need one thing to fix this; a digital mic to trick the game into thinking that you have one. There's a popular paid option out there called VAC, but it's kinda pricy. Luckily, I found a free alternative called VB-CABLE Virtual Audio Device[vb-audio.pagesperso-orange.fr]. Scroll down on the page and click the first orange download button.

Extract the ZIP file and run the setup that matches your PC type (x64 PC's use the x64 setup while x32 (aka x86) PC's use the normal setup). Install it, and you should be good to go! But, it's best to make sure that it worked, so go to "Control Panel\Hardware and Sound\Sound" and check the "Recording" tab. If everything went right, you should see something called CABLE Input.
Congrats, you're ready to go! Enjoy SWBFII!