For the few folk you discovered that they couldn't use Game Studio Connect after they got a repaired Xbox a patch is finally imminent - today March 12th 2008. Its been a while since the bug was found but remember everything that runs on the xbox 360 has to go through the Xbox cert process which isn't always a speedy process.

Michael Klucher Program Manger - XNA Community Game Platform

We just wanted to give our XNA Creators Club members a heads up that tomorrow we'll be releasing a title update for XNA Game Studio Connect. There are no significant new features in the update, however this should fix the issues that several forums users have experienced with XNA Game Studio Connect failing to run when they have had their console repaired or used XNA Game Studio Connect on another console. The update will be applied automatically and if you have had previous problems your connection keys will be reset.