Or if your old computer with a CD / DVD drive is still working, you should be able to copy the contents of the original installation disc onto a USB drive, then plug that into the laptop, and run the installation program from there.
As a rule, copying a Windows program's folder from one computer onto another won't work seamlessly, as there are often various registration files etc created during the installation, and these may be specific to the machine on which the program is installed, and / or may be located in system / hidden folders, etc.
Stellarium is a very good free, downloadable planetarium program - well worth a look, even if you are successful in getting your existing software installed onto the new machine:
https://stellarium.org/
Good luck!