It does not seem that it detects your sound card or the drivers aren't installed.
Uninstall the sound card drivers you have from Device manager, then download and reinstall the drivers from your manufacturer site (for your model you have realtek) from here:
http://support.gateway.com/us/en/emac/product/default.aspx?tab=1&modelId=1461
If that didn't work and, if the mixing device error happened recently, you can try to use System restore to an earlier point.
Look in Right click My computer> System restore and see if the disable system restore isn't checked.If it is uncheck it.
Volume shadow copy is related to backup in Windows, ironically, including with System restore service (for which the Volume shadow should be enabled, started and checked in computer management>services and msconfig also along with System restore service), and has nothing to do with the actual sound settings.
If System restore still doesn't load, then you could try running it from Safe Mode.