Like Greengolfer15 I am not from Laminar Research either. Just a flight simmer from down under.
Like you, I have a disc version of X-Plane. There are two legal disc versions. A version from Laminar and the second version provided by Aerosoft under licence from Laminar to sell in Europe and the South Pacific.
I have the Aerosoft version. My assumption is you have the aerosoft version. In the box I found a small card/brochure with an alpha/numeric number listed. It is not an activation key to run X-Plane. It is a ploy/conn/ enticement/encouragement by Aerosoft to purchase other products from them at a 15% discount. Like you I thought it was an activation key only to be told via Laminar that it was not.
As Greengolfer15 has advised you, to run the DVD version you have to have disc 1 inserted in a dvd drive at all times when running your current version of X-Plane. If you don't the software will not work. You also need to be connected to the internet on a regular basis. If you don't, X-Plane will shut you down because the software performs a silent background check to ascertain if you have a legal copy and how many legal versions you are running at the same time.
Using your disc version, you can install X-Plane on any number of computers as you like but you can only run one legal version at a time. This means you can install X-Plane on your second computer and use the inbuilt DVD drive.without any problems but not able to run XP on your current PC.
As Greengolfer15 has indicated in his option 3, you can download the digital demo version onto your new PC and when you run X-Plane you will be asked if you have a product key or a DVD. If you say no to each question when asked you will be locked into a demo version. I have used this method to install X-Plane on another Laptop not associated with my X-Plane PC.
If you intend to run 2 copies of X-Plane at the same time on your current PC and the new PC, then you will have to purchase a second legal copy. If this is the case I would suggest you run the disc version on your new PC and purchase a digital version for your current PC.
Remember, all PCs running X-Plane have to be connected to the internet. More so (at all times) with a digital download version.
Welcome to the world of X-Plane and good winds