Hey, this has happened to me also. Brand new xbox for christmas, set up live, and accounts that day using the free month subscription. played it for the day.
next day tried to log in and redeem the 12 month gold i'd bought and the 2000 points, but couldn't get on. Connected to internet but not xbox live. The day after that it would not even connect to the internet (just the wifi).
Have tried every troubleshoot solution on the website, tried calling the number which does'nt exist, couldnt leave my number cause it said it wasn't a valid number, tried an ethernet cable, tried another router at a different location, also have rung my internet provider and they have said it's fine.
My poor son has spent so much of his own money and has still not enjoyed any xbox live, he can't even play multiplayer on black ops II.
I can't believe i haven't been able to talk to a person about this.