It appears from your last post that you want to use the mobo's Realtek sound output system, and not the system in your video card. (It is also noted that your list of possible audio output devices does not include something on the vid card, so maybe its driver has not been installed. However, we'll skip that.)
If Windows is trying to use the Realtek system but you still have no sound, try this. The background is that many Realtek systems have a feature that allows you to re-assign output jacks to different functions. We are talking here about the several 3.5 mm jacks on the back panel of your mobo. The way that system works on my machine and many others is that there are some interactive dialogs you MUST respond to in setting things up. If you don't, the default action by the Realtek hardware is to send out NOTHING, so you get silence. So, try these steps to fix.
1. Unplug all the things plugged into the rear audio jacks - speakers, headphones, mics, external audio inputs, etc. Reboot your machine. This will cause the system to revert to assuming that NOTHING is plugged in and it all needs to be re-adjusted.
2. Arrange your system so you can have access to the plugs and the jacks on the back, and also see your screen. Boot the system into Windows.
3. ONE socket at a time, insert one plug. For example, plug your front left/right speaker plug into the green Line Out socket. Now check the screen for a pop-up window. It usually says it has detected that something was plugged into the green audio socket, and asks you to confirm what that was. It probably will suggest that it might be front speakers. You have two choices. You can click on "Yes" to confirm the suggestion, or click on something else to change that. Then click on OK to finalize that. BUT you can NOT just ignore it and let it use the suggestion. It won't. If you ignore the window, it will disappear and the system will NOT send any signal out of the green socket because it still has NOT been told exactly what was plugged in. You MUST answer and click the OK button.
2. With that done, go on to the next. Plug in something else - maybe your front center/subwoofer plug into the orange socket. Again, go to the new pop-up and confirm the correct device that was plugged into that socket.
When you have plugged in all your devices, try your system. Perhaps pop up the Realtek configuration utility and use its built-in test/demo panel. Your system should be able to output sound via your speakers.
I'm not clear where you are plugging in your headphones. It could be into a front panel headphone jack, into one of the rear panel jacks, or into a jack on your speakers. The front panel jack is the most common. For that to work, of course, you will have to have plugged some connector from inside the case front panel to a mobo Front Panel Audio Connector. Further, the mobo port used often can output to either of two front audio panel types: legacy AC '97 type, or Azelia HD audio type. Check your case's manual to find out which type of front panel audio jacks it uses, and you'll need to check the BIOS setting to match.
Now two things to check in BIOS Setup regarding the mobo's audio output configuration. In my system, these are found in the section for onboard devices. For the audio system, check to ensure that it is set to the correct front panel type: legacy AC '97 or HD Audio. Then also look for an option (IF you have it) about what the system does when headphones are plugged into the front panel. SOME systems let you choose whether plugging headphones in there automatically kills your speakers, or leaves them operating. After you have set these options in Setup, remember to SAVE and EXIT.