Here are the typical layouts for the iTunes folders:
In the layout above, with the media folder (everything in the red box) inside the library folder, the library is considered to be portable. A portable library can be moved from one path to another without breaking the links between the library and the media and being self-contained is much easier to backup.
My guess is that all you have is the stuff inside the red outline, but not the rest. I.e. not everything that made up the working library on the old system.
If I'm right, and it is too late to recover the missing database files from the old system, then I would suggest you use the shift-start iTunes method to create a new library at <External>\iTunes (rename the current folders at the root of the drive if you already have an iTunes folder there). Then move the contents of your old media folder inside <External>\iTunes\iTunes Media. Finally use File > Add Folder To Library and add the iTunes Media folder.
This should import everything into your library, with the minimum of files needed to be copied, moved or renamed.
tt2