If you have the latest drivers and all cables have been checked it will be a case of seeing what is at fault.
Check that both Monitors work on the VGA connection to see if they work.
Connect one monitor only using the VGA/DVI adaptor to the DVI do you get a picture when booting? try other monitor as well. If no picture fault could be with the adaptor or Video card. Try adaptor on another computer if possible.
Yes, second monitor is fine, powered up (and works on the VGA)
Identical monitors have VGA only input. Card has VGA, HDMI and DVI-D. However, reading the spec on the converter (which is in odd translated Chinese) it sounds as if I can't get an analogue signal from it??