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Go to setting and then Time & Date. Then change it from manual to set via internet. That should fix it, if that doesn't work hit triangle on the PS Store icon and delete itt, then reinstall. Hope this helps.
Maybe restore everything back to default and see if it lets you set time & date via internet afterwards. Sorry for skimming your post, the format just hurt my eyes to read entirely.
I'm about to give up. I guess as long as I can play Last of Us and the PS1 & PS2 classics I downloaded, that will have to do.