Many motherboards do not have onboard video. Have you tried both DVI ports? Make sure the VGA cord is attached firmly to the adapter and the monitor. If the monitor has multiple inputs (my Dell monitors have HDMI, VGA, and DVI inputs) make sure you select the right one. Also if your graphics card has power inputs, make sure they are connected to your power supply. Higher end graphics cards will have one or two PCI Express power inputs which must be connected for the card to work.
If you have another monitor (or TV with HDMI) try hooking it up to make sure the monitor isn't the problem. Similarly, if you have another VGA source (another desktop, a laptop, netbook, etc) try plugging it into your monitor to make sure your monitor works. If the monitor works fine on another system, the problem is your computer/graphics card. If your computer works fine on another monitor, the problem is your monitor. It could also be a bad VGA cable or (less likely) a bad adapter.