First off. AWESOME UPDATE, finally you got your head out your asses and listened to us (somewhat...I could have done better personally but whatever, not important).
When I try to play your broken game it says "You must be signed into Xbox Live in order to play Destiny".
I'm connected to Xbox Live Bum-Fuçks. Fix this. Now.
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Reset your router and modem. Strict NAT setting causes this.