Can't connect to App Store or iTunes Store

Question

For the past two days, I haven't been able to connect to the App Store or iTunes Store. This is happening on all Apple devices connected to my home network - a new iMac, iPad Air, and iPhone 5. Every attempt to open the App Store or iTunes Store results in a spinning wheel for a few minutes followed by an error message "Can't connect to the (App/iTunes) Store". The App Store will display the Updates and Purchased Items, but that's all. It will not open Featured or Top Charts. I have tried with wifi and with an ethernet cable to connect the iMac. Here's where things get weird. My iPhone will open the App Store and iTunes Store if I turn off wifi and use LTE. I can do the same with my iPad if I use the iPhone as a hotspot. I connected the iPhone to two different wifi networks away from home and had the same issue... works over LTE cellular, but not wifi. In addition to this, all of the Apple support pages load extremely slowly, I am using an Airport Extreme as router. I've reset the cable modem, reset the router, reset network setting on the devices, powered down all devices, etc. All other web apps and web pages load just fine. Only those related to App Store, iTunes and Apple Support seem to be affected. The Apple main and product pages also load with no problem. Is anyone else having problems with the App Store and iTunes Store? Is there an obscure setting somewhere that I'm missing? Everything was working fine until a couple of days ago.

Answer 1

Back up all data.
Unlock the Network preference pane, if necessary, by clicking the lock icon in the lower left corner and entering your password. Cllck Advanced, open the DNS tab, and change the server addresses to the following:
          8.8.8.8
          8.8.4.4
That's Google DNS. Click OK, then Apply.
In Safari, select
          Safari ▹ Preferences... ▹ Privacy ▹ Remove All Website Data
and confirm. If you’re using another browser, empty the cache. Test. Any difference?
Notes:
1. If you lose Internet access after making the above change to your network settings, delete the Google servers in the  Network preference pane, then select the TCP/IP tab and click Renew DHCP Lease. That should restore the original DNS settings; otherwise restore them yourself. Remember that you must click Apply in order for any changes to take effect.
2. I don't use Google DNS myself, though I have tested it, and I'm not recommending it or any other DNS provider; the server addresses are offered merely for testing purposes. There may be privacy and technical issues involved in using that service, which you should investigate personally before you decide whether to keep the settings. Other public DNS services exist.