No Apple devices can access the iTunes or app stores on my home network?

This is an odd problem I haven't encountered before. The internet is fully functional, but whenever I try to access iTunes or the app store on my iPad, iPhone, or sister's iPad, it says "can't connect to iTunes store."

I'm having the same similar problem as you my computer internet is really good super speed searches and all that, i can access the itunes store but when i go on my ipod touch (4th gereration) i can get Wi-Fi but it just does not load? I can't go on e.g. Youtube app, app store, safari its pretty odd and its a major issue to me.
But i think i can solve your problem
Go to itunes
Click on Help
Click on Run Diagnostics
Click next
And there you have go
Now if it ever comes up with a red circle it will have a help button that your problem may be.
Contact me if that works or you want more ideas
I've tryed all of them but somehow does not seem to work for me on my Ipod touch
But Hopefully it works for you Good Luck!

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