The ACDs only take digital signals. Unless you have a 360 with an HDMI, you won't be able to connect it without an expensive box.
DVI can carry analog signals, with the 4 pins surrounding the long horizontal pins. If you take a look at your ACD connection, you will notice those missing. What that means is that anything from analog to digital (component, vga, etc) will not work as the pins for an analog signal just aren't there.
So again, if you don't have a 360 with an HDMI port, you are out of luck, at least in terms of a cheap solution.