though *LucidLogix Virtu MVP* is first mentioned it was discontinued so forget it.
the idea is that i want you to remove discrete GPU first, install HD4000 driver, add fake display to the unconnected onboard HDMI, then insert dGPU back to mobo.
if in device manager the HD4000 still shows issue, i wonder if your mobo is at fault such that the onboard graphic ports are starved from electricity/signal when the PCIE/PCI slots are occupied