n,
An upgrade always build on a qualifying earlier version (maybe among a number of possible ones), so you also need a serial number for a qualifying version.
To have and use it legally, you must have the qualifying version. The original price of the CS2 has been lower because it was an upgrade; and in addition, both serial numbers must be unregistered, or a licence transfer would be needed, which would obviously be impossible unless the garage seller were the licence holder.