Yes, it will work. No there is nothing wrong with having both connectors attached, however, the monitor will probably default to using the VGA (Dsub). You don't need to use the VGA. Just remove the VGA cable from both ends and just use the DVI cable by itself. You will have a better video image and Windows 7 just works better with a digital signal to the monitor.
So remove the D Sub(Blue cable) and keep the DVI(White Cable)?