NIS / N360 Mix-up?

I received my new Toshiba Computer to replace a 7 year old HP yesterday.  The Toshiba package that I bought online included one month of Norton Internet Security.  Obviously the scheme is for me to order a year's coverage.  Well, my problem is that I registered the Norton Internet Security program.  My internet address was reguired for completion of registration.  I then received a prompt to activate Norton 360.  This program was valid until June 2012.  When I tried to download, I received a prompt telling me that this was an older program than the Norton Internet Security and that I couldn't download.  I am wondering if the system is getting confused with my old HP computer.  I have Norton 360 in operation on the old computer registered to the same email address.  Should I delete Norton Internet Security and load Norton 360?  I don't plan to use my HP computer anymore.