The blue connection is called D-Sub, DB 15, or VGA.
Is your blue monitor cable connected to your computer directly? Is it near the top outside edge of the computer (by all the USB / mouse / keyboard connections) or near the middle of the computer. If the answer is yes and near the top, then you are connected to your integrated graphics. Integrated graphics should automatically turn off once an add-on video card is detected
Most gaming video cards don't directly support VGA and come with a converter. Locate the converted and connect it to your video card, then connect the monitor to the converter.
DVI to VGA convertershttps://www.google.com/search?q=dvi+to+vga&source=lnms&tbm=isch&sa=X&ei=HMt5UaKrCunqiwKx74HQDg&ved=0CAoQ_AUoAQ&biw=1044&bih=848