Have someone else attempt to sign in using their Apple ID. If they can successfully sign in and use Messages/FaceTime, it may be your Apple ID.Someone I know had this happen and I was able to sign in usingmy Apple ID. After a call to Apple Support and then being elevated to a tier 2 support person, it turned out it was a problem with their Apple ID. It took the software engineers 3-4 days to fix the problem. When calling Apple, make sure you tell them it is an Apple ID problem so you don't get charged.
There is a contact link.
Apple ID Support
Apple ID Support (2)
Apple Support by e-mail or chat Select your device, Battery, Power and Charging, then Power adapter not working to get a chat option.