As James mentioned, do you still have the OLD Mac so that it can be turned on?
My suggestion:
- Get an external drive large enough to hold the library
- Boot up the OLD Mac
- Connect the external drive, go to your home folder, and copy the iTunes music folder to the drive (using the finder). DO NOT USE TIME MACHINE
- Take the drive to the NEW Mac and connect it. Let the icon mount on the desktop.
- Open the drive icon so that the (old) iTunes folder is visible.
- Now open iTunes (or Music) on the NEW Mac, and see if the import function will work.