See the Apple Support article(s) below.
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.
Restart your iPhone, iPad, or iPod touch *
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.
Restore to Factory setting. *
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.
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. -
Apple on Twitter -