Graphics card detected by windows, but mini-HDMI port is not working on boot

Graphics card (MSI 550 ti) has 3 outputs, 2 DVI and 1 mini-HDMI. It used to be coected to an HDMI display using the included mini-HDMI to HDMI adapter, and a standard HDMI cable.

The cable itself is not the problem, since it works when coected to HDMI output of onboard IGP. On booting into Win 7 using the IGP, I can run gpu-z and get statistics of the GeForce 550 ti shown as well - so the card is being detected after bootup.

I don't currently have a DVI-to-HDMI adapter or cable to test, so I want to know if there are other possible fixes to get the display working again using mini-HDMI port.