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See if the Apple Support article(s) below helps answer your question. The links contain troubleshooting steps you can try.
If you can’t turn on or sign in to iMessage or FaceTime. *
Some things you can try. Do you have access to another WiFi network where you can try? That has worked for several people.
Try a restart.
Try a forced restart. See the section towards the end of the article.
Reset Device. -
If necessary
Hard reset. -
Do a backup and try a factory reset. Then restore from the backup. See the articles below for instructions.
Restore - If you see an error when you update or restore your iPhone, iPad, or iPod. *
Backup - Restore your device from an iCloud or iTunes backup. *
If you still have problems, 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 using my 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.
You can also try signing in on another device/computer. There have been a couple of posts where people's device/computer was blocked. You will need to contact Apple for that problem.
There is a contact link.
Apple ID - Official Apple Support. -
Contact Apple for help with Apple ID account security - Apple Support. * (The link doesn’t always load)
Get Support - Work through the screens to get a chat option.
Apple Support schedule phone call. -