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Not really much help, but
I had the same problem occur today for me. I haven't a chance to call Verizon about it. I have 2 xbox 360 and neither want to connect to live, neither does Games for Windows Live on my PC. My xbox one connects fine with absolutely no problem. I hoping it fixes itself tomorrow. I am trying a few more things myself before I call tomorrow when I get off work. I will post if I get anything to fix it. I hope you would post if they come up with solution i before get the chance to call myself.