i had the same problem for days i did the following
go to windows live and see if it will allow you sign in, if it say your account is blocked then this is why your xbox cant log on, i think, dont ask for a text message to your cell for a reboot code it didnt work for me i waited 2 hours for a text.
what i did was get a new gamer tag by signing up again but with a hotmail account, i had a yahoo account and maybe microsoft doesnt like that i dont know.
then i got onto the game console and downloaded my new gamer tag and everything worked fine,
just a small glitch in the system or something i did wrong in setup, but working fine now.
warning dont do what i did, i entered my codes for the games i got with the system into my account that i thoiught worked then found out it didnt and i had to spend 3 hours on the phone to retrieve the codes and it will take several days for them to get them back to me,
my fault tho i should have made sure the game was working first, all is good