I have an article here that addresses this sign in issue with FaceTime and may have some troubleshooting steps to help you resolve this issue:
Try the following:
- Ensure that you have an active Internet connection.
- Verify that you are using a valid Apple ID at appleid.apple.com. You can also create an Apple ID or reset your password from this website. Other things you should confirm while logged into appleid.apple.com:
- Confirm that the email addresse(s) for your Apple ID has been verified.
- Check for miss-types of the email address
- Check the spelling of the email address
- Check that all letters are lower case
- Make sure that special characters are correct, e.g. no commas (,) where there is supposed to be full stops (.), etc.
- Note You may experience issues if your email address is associated with more than one Apple ID. If you have multiple Apple IDs, log in to appleid.apple.com with each Apple ID and confirm that each email address you wish to use for FaceTime or Messages is associated with only a single Apple ID.
- Make sure the date, time, and time zone are set correctly in Data & Time preferences, in System Preferences. Tip: Enable "Set date and time automatically" in Date & Time preferences to automatically keep this information accurate.
- If third-party firewall or port filtering software is installed, it needs to be configured to allow connections to apple.com, verisign.com and verisign.net. A list of ports required for using FaceTime and Messages is in Using FaceTime and iMessage behind a firewall. Please consult this article for further help configuring firewalls and Internet security software.
- If your /private/etc/hosts file has been modified, make sure that it is not interfering with communications to apple.com, verisign.com or verisign.net servers. Note: Some third-party software installers may modify the /private/etc/hosts file without alerting you. Instructions about how to check and resolve issues with a /private/etc/hosts file are in the "Blocked by configuration: (Mac OS X/Windows)" section of iTunes: Advanced iTunes Store troubleshooting
Thanks for being a part of the Apple Support Communities!
Hi again KateD14,
Thank you for using the Apple Support Community. Due to the nature of your issue or question you may find more information by using another one of Apple's support resources - https://getsupport.apple.com/GetproductgroupList.action.
I FOUND THE FIX!!!!!
Back up all data.
Triple-click anywhere in the line below on this page to select it:
Right-click or control-click the line and select
Services ▹ Reveal in Finder (or just Reveal)
from the contextual menu.* A folder should open with an item selected. Move the selected item to the Trash. Log out or restart the computer, empty the Trash, and test.
*If you don't see the contextual menu item, copy the selected text to the Clipboard by pressing the key combination command-C. In the Finder, select
Go ▹ Go to Folder...
from the menu bar and paste into the box that opens by pressing command-V. You won't see what you pasted because a line break is included. Press return.
Basically drag the items in the identityservices folder to trash log out, log back in, empty trash, start messages or facetime!!