After installing Mountain Lion, iMessages and Facetime does not work. When I try to sign-in I get a message that says: The server encountered an error processing registration. Please try again later. Apple care does not know what is the cause. Please help

After installing Mountain Lion, iMessages and Facetime does not work. When I try to sign-in I get a message that says: The server encountered an error processing registration. Please try again later. After 4 calls to apple and 8 and a half hours on the phone. The apple people does not how to solve the problem. The last thing they told me is that they will send the problem to their engineers and I will hear from them. unfortunately they have not contact me.

During the phone calls I tried putting the date and time in automatic, changing the username and password, I even tried using somebody elses username and password. Please help, facetime is my tool to telecomute, and it is hurting my job.