Have they had a service outage in your area? That would explain it, and you'd just have to wait until it was fixed.
Have they checked your SIM card? A defective card will give that message. (So can a spec of dirt on the wrong spot on the card or one of the card contacts.)
You're probably going to have to bring it into a store to have it checked out. Tech support (I suspect you were talking to level 1 customer support, which is less useful than the phone manual - which is usually good only for wrapping small fish) should have told you that.