Tech support scam originated from use of product key

I bought a new computer and wanted to install my Norton Security with back up.  I went to the site, it asked for my product key.  I inserted it.  Then a Norton error message came up.  It said it couldn't accept the key and gave an error code.  It said if you receive this message, call the following 800 number.  I did.  The person who answered said he was with Norton and transferred me to a high level Norton tech support person.  That guy said he would check the key and call me back.  He called back and said the key was fine.  It was probably something in my computer.  He was concerned it was some type of infection that Norton Security didn't catch.  He said that they only deal with it when someone like me comes back with that type of problem.  I had had Norton fix other infection problems in the past so I felt comfortable in letting him onto my system with a standard control tool.  He did an "analysis'  and let me watch the results.  First the text turned red as he scanned through.  He said "Oh, oh, it's the Russians with their ccrr.exe"  Then he continued and the screen text turned blue.  He said, "Oh,oh, it's the blue screen of death, its the Chinese."  Since I thought that I was dealing with Norton, I was concerned.  He said this was something that a tech at his level couldn't handle.  He said he would contact an outside group, USA Techdesk, and see if they could handle it.  He called back later and said, "Good news, they can take care of it and do it today.  Since they are not with Norton, they need to charge for it.  It was usually over $1000, but for Norton they would do it for $350.  Again, thinking I was dealing with Norton, I agreed.  Then he wanted to sell my a follow up check on a regular basis to make sure it would happen again.  At this point I became suspicious.  I said do you work for Norton?  He said of course, here is my employee number.  At his point, I was feeling quesy but agreed to let the clean up begin.  He said it would take about two hours.  Offline, I discussed the situation with my son, who is an executive with a sophisticated computer firm.  We agreed it was probably a scam, and immediately stopped the control of my computer by cutting out the internet.  The "Norton" guy immediately started calling.  I answered and said I didn't think he was with Norton, he insisted that he was and hung up on him.  I called my credit card company.  They will suspend my payment and give it to their billing dispute people.  Hopefully, I wont' have to pay the scammers.   HERE IS THE BOTTOM LINE: I got to these people by trying to get my Norton product installed on my computer.  Somehow, they were able to fool me into thinking they were Norton, when they were USA TechDesk all along.