Thank you for using Apple Support Communities!
I understand from your post that you have not been able to update to iOS 11, login to Game Center or iCloud. The following articles have steps which address issues with both Wi-Fi and Cellular connections. Using these steps may help refresh your networks and allow you to connect to Game Center and iCloud.
If your iPhone, iPad, or iPod touch won’t connect to a Wi-Fi network - Apple Support
If you see No Service or Searching on your iPhone or iPad - Apple Support
Best Regards.