I just bought a brand new DH77KC and am having issue with the integrated graphics. I have an I5-3470 quad core which supports the HD graphics. Whenever I connect to the DVI or HDMI ports, the system either 1.) will show no video OR 2.) will spin the fans very briefly and then shut off again. The odd thing is that when I reset BIOS default AND use a PCIe x16 graphics card, then the system will boot. Once I get it booting, I only turn off power, remove the PCIe graphics card and then connect the monitor to the DVI port and turn power back on again. But, the board never comes up?!! I am getting VERY frustrated by this as I bought an Intel branded board because I thought it would be more reliable!
I'm sorry to hear that you are experiencing problems with the motherboard but we can try to fix them.
First thing to to is test the system on a basic configuration, remove any devices that are not required for the motherboard to POST like hard drive, optical drive, card readers, front panel USB and extra memory. Only leave on the system the processor, the Heat Sink, one memory stick and the power supply. On the back only connect the keyboard and the monitor. Test the system, if it boots normally then start adding parts to find out which one is causing the behavior.
In the case that the system has the same behavior on a basic configuration, make sure that you load the BIOS defaults, that the BIOS is updated and that the temperature readings in BIOS are normal.