I have a 19 LCD Monitor, this one
You might be able to use the VIVO cable you are describing to get the Wii video to show up in a window using video capture software, but its going to look like crap, because its only running it at television resolution, which is basically 240 horizontal lines. A better option is to get the Wii Component Cable (like the yellow, red white, but its red, blue, green, white, red). They cost about $25. You connect the component cables to another converter called a 'Component to VGA Converter'those are a little more expensive, but if you google that term you should find what you need. This will basically double the video resolution and make the picture look a TON better.
No. Everything on that video card is an output. What you need is an input on your system or on the monitor that the Wii can connect to. That would be: Composite video (Single yellow RCA socket) S-Video (Mini Din socket) Component Video (R + G + B RCA sockets) Your monitor has VGA and DVI-D inputs so you can not connect directly to the monitor. Your video card has all outputs so you can not connect to it. The three coloured wires are component video.