unplanned bacon :
panathas :
Make sure that you are plugging your monitor to the GTX 780 and not the motherboard. You should get in the windows safe mode and uninstall the NVIDIA drivers and Intel GPU drivers. Then log into windows and reinstall the latest NVIDIA driver you can find. Why do you want to use the iGPU. It doesn't offer you any advantage over the GTX 780 and you only have one monitor. Having two completely different GPUs working at the same time complicates things and needs two separate drivers that may cause issues like what you are experiencing right now.
I was trying to isolate a problem with a game not booting, so I wanted to see if it was the graphics card at fault. That's when I found my integrated doesn't work, or at least doesn't work for long before dying.
If you want to only use the iGPU you have to uninstall the NVIDIA drivers, shut down your system, turn the PSU switch off, remove the GTX 780 from your motherboard, connect the monitor to the motherborard, boot the system, log into the windows and finally install the Intel iGPU drivers. That's the correct way to do it, if you want to only use the iGPU, and not what you were trying to do. As you can see, I don't think it's worth the hassle. If you try to use the iGPU while you still have the NVIDIA card, plugged in your motherboard, the BIOS will likely disable it. That's what is happening right know and I think that the integrated iGPU is fine and it should work properly if you follow all of the above steps. If it still doesn't work it may be disabled in the UEFI BIOS and you should manually enable it.
If a game doesn't work with your GPU, update the NVIDIA driver to the latest version you can find. Also make sure that this specific game is updated/patched to its latest version as well. If this game is a pirated version I don't think I can help you any further and this is the most likely root cause of your issues and not the GPU.