Can’t access App Store on Apple TV 4

Do your network connects to the Internet?

You need Internet access for the AppleTV.

Try reset:

If you have an Apple TV (4th generation): Disconnect the power and HDMI cables from Apple TV. Connect one end of a USB-C cable (sold separately) to Apple TV and the other end to your computer. Open iTunes on your computer, select Apple TV in the Source list, then select Restore. If that doesn’t work, contact Apple TV Support.

Are you connect to same Wi-Fi network at home?

Did you also try Ethernet connection?

If Apple TV isn’t responding, try restarting it.

Restart Apple TV. Do any of the following:

• Press and hold the MENU and Home (tv icon) buttons until the Apple TV status light blinks rapidly.
• Disconnect Apple TV from the power outlet, wait five seconds, then reconnect it.
• In Settings (gears icon), go to System and select Restart.

I just installed tvOS 11.3 beta 2 (15L5175d) and it works again.

You didn't mention above that you were running beta software. Any issues would need to be reported through the proper feedback channel, or you can restore to the current public version of TVOS

I am experiencing the exact same problem on Apple TV 4 gen. I haven’t been able to access the App Store for the past 2-3 days. I contacted Apple support on Twitter and but they were not very helpful:

“We'd like to get this headed in the right direction so you can get back to enjoying your Apple TV. For this issue, please reach out to our Apple TV Advisors. You can reach them using our link here: http://apple.co/GetSupport”

Make a genius bar appointment with Apple for an evaluation.

Did you restore via iTunes?

i have 11.3 and app store doesn`t work. 😟

See above