I'm a firm believer that the operating system used is always a factor, along with the versions of programs and plugins used of course.
When you say "copy the installed files" from your old computer, I'm a bit fuzzy about what you mean. If you mean "copy the plugin folder of the installed plugin" from your old computer, I'm not sure that will work but you could give it a try. But I suspect that the plugins would have to be freshly installed on your new computer.
What you CAN'T do is copy the installed files of your older versions of PSP. You have to have the installation files on your new computer for the older version of PSP to install it on your new computer, so if you have those installation files saved on your old computer or on disc you can place them in your new computer and then install the PSP program from them. All PSP program version (including Jasc, like PSP9, and Corel) exist comfortably side by side.
So first install your older PSP on your new computer. Then take your old install files of our plugins, put them into separate folders on your new computer (e.g, a folder named LEGACY PLUGINS TO TEST, or something like that), and then try installing those plugs individually into your older 32-bit PSP version (if they won't install in your latest 32-bit Corel PSP version). Then make sure they work in your older version of PSP and, if so, follow the instructions from my first post.
I presently have those plugin folders that I COPIED directly in the X7 Plugins/EN folder, but you could just as easily have them in MY PSP Plugins folder as long as you point the File Locations to that folder. If they work in the programs plugin folder then they should work in any folder you point your plugins file locations to.
As I said, not all plugs will still work with this workaround but some good ones seem to for me. And for older ones make sure to get the Mscvrt10.dll just to be safe, not to mention having the plugin.dll in your Windows/Sste32 folder.
Let me know if you have further questions, and I look forward to hearing if any of this worked for you. I, for one, was surprised that the Alien Skin 7 plugins worked in X7 after I installed them in the trial of PS CS6 and then copied their folders into the X7 plugins folder (because Alien Skin says they no longer support PSP), but it just goes to show that the plugins do work with X7 but that the plugin developer doesn't want to support them in programs other than Adobe and therefore won't create an installer to recognize other graphic programs. JMHO
Regards,
JoeB