Get this moved to the proper forums. There are forums for notebooks and the others. And we are end users.
The problem, in most cases (unless the case has been changed motherboard or things like that), when messages and Facetime fails, it is because the "hosts" file has changed voluntarily or involuntarily as there are programs that change without asking.
1. Make sure the time is set automatically (System Preferences> Date & Time)
2. open "Terminal" (or from spotlight type "Terminal" and abirla)
wrote the following:
sudo pico / private / etc / hosts (if you do nothing hit enter)
3. Will appear "Password", which we type our password logon, to give us permission to modify this file.
4. With the arrow keys, search any line on which are the words "apple.com" or "verisign.com".
5. We introduce at the begining of the lines that contain one of those words, the # sign, and a space. at the begining of the lines, ok?
6. Once we have written the corresponding # in lines with the words I've written before, press CTRL X, then Y (to save changes), then press (enter).
7.Close Terminal entirely.
8. Open FaceTime and connect with the Apple ID and .... voilà! Online!
Best regards, and I hope this will be your solution!