Cannot login FaceTime/iMessage on any apple device

I get "An error occurred during activation. Try again." when I try to sign into FaceTime or iMessage. The last time I used this apple ID to do FaceTime was more than a year ago, but it worked fine at that time. But now it just keep giving me the error message. It doesn't matter what device I use. IPhone, MacBook, iPad, all give me the same error under WiFi or cellular network. I have tried everything google told me, auto timezone, DNS, network settings, etc. Frustrated....

However my apple ID works in App Store. ICloud also works fine. I have been working with an "Applecare Senior Technical Advisor" for 3 weeks and he can do nothing to get my FaceTime/iMessage work. The only conclusion he has made was this problem is related to my apple ID account.

Anyone has the similar experience before?