I have been trying to access my Destiny account on my PlayStation 4 console for around 3 months now and each time I get your error about network problems and 'permissions' have changed. I have been a PlayStation Plus member for years, All my other online multiplayer games work perfectly fine. I'm not signed into any other console as far as I know, I'm using a wired connection and my NAT type is 2, I've reset my modem and router, rebuilt my databases and restored my licenses on my PS4, I've even deleted and reinstalled the game. Nothing is helping and I just want to be able to play by the time Year 2 gets going.
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Try this: https://www.bungie.net/7_How-do-I-clear-the-cache-on-my-console/en/Help/Article/12539 Also your NAT needs to be set to Open or 1.