Moved to Norton 360 Board for better exposure.
What is the name of the service that you purchased the service contract from? Did you originally contact them, or did they initiate the contact by cold calling you?
Hello
What was the telephone number that you called? If we know the number, it can be traced to see if it belongds to a Norton company or service. The last time I had a Norton person remote in, it was neither with Skype or TeamViewer, but Norton might have changed programs over the years.
This sounds like you did not have a legitimate Norton service contract, but a service that offers support for Norton products and probably many others.
Or as SendOfJive says, it could have been some scam.
If you can supply the web link or phone number you first contacted, we may be able to help identify what is going on.