I just purchased PSE 10 on eBay. It installed fine, but I can't seem to register the product. If I understand correctly, it is probably because the original owner (not the person I purchased it from on eBay) did not do a transfer of product. Will this effect anything, e.g. upgrades, etc.?
Each version of the software is independent. When you are ready to purchase the latest version of the product at a future date, your PSEv.10 will remain on your computer, or, you can unistall. Note that Adobe no longer supports PSEv.10.
Since you are not a registered owner of the program, you will not be entitled to any discount if you decide to upgrade to a new version. And while the program may install correctly, I am not sure that you will be able to use the Editor after the 30 day free trial expires, if that is what you had to use to open it. The activation process has changed over the years, so I am not sure about that. Out of curiosity, how much did you pay on eBay?