I just installed a new video card and its drivers. The sound on my computer has now gone away? How can I get the sound back?

it might be that the video driver also installed an audio driver (my radeon hd3850 installed an hd audio driver) and it could be that windows set this as the default audio device.
go to control panel, sounds and audio devices, go to the audio tab and check whether your soundcard is set as the default device.

I tried ragingloli’s suggestion and she was correct, but there is no device to choose at all in the audio tab. When I roll back to the old drivers the sound works the devices reappear. But when I reinstall the video driver the sound card disappears as a choice in the drop down. The drop down is blank. What now?

go to the device manager and look if there are any hardware conflics (yellow triangles with exclamation marks)