I'm not sure you can really do that. VGA is an analog signal. I'm guessing you wanted to use the VGA to DVI-I adapter that comes with almost every computer video card. The only problem with that is that the adapter does VGA to DVI-I and HDTVs, at least the tvs my friends and I have, have only DVI-D connectors. That means Digital signal only. DVI-I can transmit both analog or digital. Now it sounds like it still might work but it won't because of the connectors. The adapter in question is, like I said, DVI-I and those include 4 little pins surrounding the big flat pin. TV's with DVI-D female connectors are missing those 4 pins so you cant insert something into holes that do not exist. Also I'm pretty sure the adapter does not convert analog into digital signals so breaking off those 4 pins will probably not work since those 4 pins will be transmitting the analog signal from the VGA, or at least part of it.
The only way I see of converting VGA analog into a DVI-D digital would be a converter box. Microsoft would probably release another 360 cable for hdmi if all this is correct but who knows.
If my little explaination was poorly written, the images from this should help.