Hello Keshav,
Thank you for keeping us updated on the status of the issue.
I would suggest you to try following article and check if it helps.
Connection error with Games for Windows Live
http://forums.xbox.com/gfw/xbox_on_windows/f/3042/t/1394752.aspx
If it does not help, please post question on Xbox forums.
http://forums.xbox.com/xbox_forums/xbox_support/xbox_360_support/default.aspx
Thank you