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The MOBO's HDMI is useless, i-Mode Z68 exception, when using a discrete GPU. 'Typical' is to use the GPU's HDMI and in non-Z68's Disable the onboard GPU in both the Device Manager and in the BIOS {Disable and/or reduce the onboard GPU's memory to as little as possible}.
Therefore, i-Mode Z68 exception, to use the MOBO's HDMI is the same as removing the discrete GPU -- the discrete GPU is serving no function/acceleration unless it's connected. So connect the monitor ONLY/Directly to the 'GeForce GT 440'.