I would contact Paint Shop Pros's support. It is probably a case where the key code is already registered and is then refused as to a new install. The support people should be able to clear the previous activation which should allow the current install to activate. Sigh, don't be surprised if they tell you that they can't do anything as your version is out of date. Be strong and refuse to accept their garbage. You MAY actually get a solution but I wish you luck.
It is also possible that it could be a case of the 2020 version now being current. Corel is known to be bad about support for older versions. They want you to go to PaintShop Pro 2020. From past experience I'd say that they will probably say how sorry they are that they can't help as they no longer have the older version available which, of course, is not true. I expect that they will give an approach in which they off you a 5% discount on the current version. At least this was the case when I contacted them to try to get the update patch for PaintShop Pro's version 10 which was before the "X" series to allow it to work properly in Windows 10. They actually told me that, since the version was no longer current, they no longer had the patch. Of course this was total garbage.
All the above aside please quit insisting on running out-dated software. You not only put your own system in danger but also all systems involved in your contacts.
Before you even go in the direction... This has nothing to do with Microsoft Windows regardless of the Windows version. This deals with Corel directly and their refusal to support versions that they consider out of date. At least Microsoft continues to offer updates to old versions of Windows even after no new updates will be put out. Corel does not follow this reasonable practice.
I currently run PaintShop Pro 2018 but am seriously considering getting rid of it due to it constantly throwing up alerts to try to get me to buy the current version. Since I paid for the thing I don't think that I should be subjected to their ads. I am seriously considering removing PaintShop Pro 20118 and replacing with the free Package called GIMP. Actually GIMP, even though free, is probably a more powerful editing package than PaintShop Pro.
https://www.gimp.org/