I have a recording system using Sonar X1 and Pro Tools MP9. I use a Roland Octa-Capture as my recording interface unit and when its attached to the PC it is automatically set as the default playback device and recording device. When I disconnect it (power off) my PC's sound card automatically resets as the default playback device and my System Mixer (same as Stereo Mix) becomes the default playback device.
The first thing I see is the Vsynth XT is set as default playback device and not your "Speakers" (sound card) which is disabled, which could be the cause of the problems.
The System Mixer/Stereo Mix (Soundblaster calls this "what you hear") is normally set as the default recording device and along with Soundblaster, what you are hearing on the speakers is available for recording. With the System Mixer whatever device is inputting, such as speakers or line in is available for recording using the System Mixer. You set your recording program to use the PC's System Mixer (Stereo Mix) as the recording source (for analog inputs).
The devices that are currently unavailable, along with the speakers suggests the PC's sound is disabled or not functioning. Correcting that should bring back the recording devices, although you may have to enable them after you get the PC sound device (VIA HD Audio) working correctly.
First step, remove/disconnect the Synth you have connected and see if that enables the sound device and recording devices. If not, check the status of the device in the Device Manager. You may have to either (or both) uninstall the VIA in the Device Manager (but not the drivers) then restart the PC and let Windows detect and reinstall the sound, and/or reinstall the correct VIA drivers either from the PC vendor or the motherboard vendor as applicable.