I'm sure the upgrade is still possible, but I'll leave the details to someone from JRiver.
Oke, so I understand you have 2 pc's, you installed a fresh copy of MC and moved a disk from one pc to the other that contains your music. Your playlists are stored in the database that JRiver uses to store all the information about your music, it doesn't move with the music itself.
I think the easiest at this point is to export your libraries on the old machine and import them on the new. You can do this by selecting a playlist and choosing Export from the file menu. Choose MPL as the Format and All for output range. Once you've exported them you can carry them over to the new pc and import them with File/Import playlist.
If you really have too many playlists to do this manually, you can also choose to carry over a library backup and restore that. But that will bring other issues like paths to music files being different that then needs fixing, but that might be less work than exporting a lot of playlists, its up to you.