Before you call your cellular carrier to be sure they're not somehow blocking, try to log in to http://discussions.apple.com
That should verify you have internet access and the AppleID itself is active. If not - you'll need help from Apple Support to reset your account or investigate if it's locked. (Or the carrier to get you connected to the internet)
Assuming you can log in, I would put the device in AirPlane mode and then change the date/time to be about a minute off what you think the time is.
settings > general > date & time
Then disable AirPlane mode and re-enable automatic time setting and see that the carrier gets your device to the correct time.
At that point, try the iCloud preference pane. That should get you a decent chance that the device re-connects to the services. Unless there is a service outage - you should have a specific error message at this point to track down for iCloud settings (or whichever of the other items using your AppleID you start with after resetting the time and network connections).