After reading the wall of text, I give you
http://support.microsoft.com/kb/908874 now this can either be a direct problem, or a NAT/MTU problem within the networking where you currently are.
When trying to access anything on the marketplace do you get any error messages at all?
Have you tried running the Xbox live Connection test on the dashboard?
This is Asuming you already have the NXE update.
http://support.xbox.com/support/en/us/nxe/xboxlive/default.aspxhttp://support.xbox.com/support/en/us/nxe/xboxlive/troubleshooting/NetworkTest.aspxSorry don't have that many answers, but those pages should help you along the way, because I would end up paragraphing more questions in one go than you can reply to. Take a look on the second link an see if you can find any extra information that is todo with your current situation.
If you need anymore help do post again.
"Information is not knowledge"
MW2: Veteran completion time: 6hours 23mins Spec Ops: 69/69