You'd have to get the Component mod done first. I guess what you're looking for is a Composite-to-DVI adapter since you have a computer monitor that probably only has DVI/HDMI and VGA inputs (New LCD TVs would have Composite, Component and HDMI inputs at the very least). Such an adapter would need to double the resolution to 480p as well. I'm guessing this particular adapter, as cheap as it is, expects 480p input at the bare minimum.
Anyway, if all you wanna do is connect via standard, shitty Composite, then nothing will beat a TV/monitor with a Composite input built in...