What happens when you try? Error message(s)? More information would help.
Messages - If you get an error when trying to activate iMessage or FaceTime.
Messages Troubleshooting.
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.
Reset Device.
If necessary
Hard reset.
Do a backup and try a factory reset. Then restore from your backup.
Restore to Factory setting.
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 also.
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
https://twitter.com/AppleSupport
