Adapters, especially dealing with old (VGA-DVI) and new (HDMI, DisplayPort) are unreliable.
For a start, check that your secondary Monitor works when connected a s primary monitor, to rule out your monitor or the port on the graphics card is damaged.
If they work, pins on the DVI-port can be damaged (i had this, still got a picture, but only in red...).
Or, as i said, the adapter might just be crap. Happens all the time. There is DVI-I and DVI-D, which may also cause problems (google that).
In case, go to your local shop, and ask if they have a replacement-adapter that you could bring back in case it is not the solution. And in case it helps, support your local shop by buying it there.