Browsing the Xbox Official Forums, I found this interesting bit of information from a user. I do not know if it is true, but it sounds like it is very plausible.
"Its a dash update issue, the version 2.0.7363.0 update was made live on Friday the 16th, and removed shortly after.
If you got the update notification on Friday, your system should still work with the storage device that you used at that time, but NO OTHER DEVICES will work.
This isnt a network issue or cache issue so dont bang your head against the wall trying to figure it out. "
Here is another quote: "Yes, this means somehow the flash in your Console was updated to 2.0.7363.0, but not your storage device.
Every time you try to connect to live, you will be prompted to download an update that has been removed from live.
Until MS releases a fix, you wont be able to connect."
Interesting. If anyone wants to look at the thread, you can find it here:
http://forums.xbox.com/25283951/ShowPost.aspx
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Holy awesome! Microsoft just recently put the 2.0.7363.0 update back on their servers. I was now able to successfuly update my console.
I can now connect to Xbox Live!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
This is glorious!