Error connexion iMessage & Facetime Macbookpro 15" 2009

There is no official public documentation of that alert as far as I know, but apparently it can sometimes mean that the primary or alternate email address is invalid. Search the Web for the phrase "My Apple ID." The top hit should be an Apple web page with that title. I'm not giving a direct link because such links are never to be trusted. Sign in and verify the ID.

Otherwise, do as the alert directs. According to reports, you won't be charged for the support call if you select "Apple ID"—not the hardware model—as the product you're asking about, and cite the "customer code" in the alert as the "validation code" when you speak to the Apple representative. I can't confirm.