Elements 10 to new Mac

Hello, and please accept any necessary apologies for incorrect protocol. I don't use these forums often. I did look extensively for the answer to this question, but did not find what I needed. I have an obsolete Mac where I downloaded Elements 10 a few years ago. I bought it from a third party seller and did not register it with adobe. Now I want to put the software on a new Mac (10.9.5 in case that matters), but I'm not sure how to get the required serial number. Any advice appreciated, including "this is way too much trouble and you should just buy a new version". Happy new year.