No Sound and Black screen Fix
I dont know if these fixes have been posted but the worked for me so I am going to put them up here and hopefully everyone that is still having issues can benefit from it.
For the "no sound" issue this is waht I did:
Go to the Control Panel, Hardware and Sound, Manage Audio Devices, and select the Recording tab.
Next, right click the empty space below the installed devices and check Show Disabled Devices.
The Stereo Mix should appear. Right click on the icon and enable it. Then, click on OK to close the window and then close the Control Panel
For the black screen erroe try this:
Go to your Library, right click on Bioshock and open Properties
In properties click "Set Launch Option..." and type in "-dx9" without the parentheses.
You should be able to run the game no problem, or atleast these fixes worked for me. I hope this helps.