Try:
Backup library (with thumbnails) on old machine. File>Library>Backup.
Locate that backup zip on the old machine (C:\Users\name\Documents\JRiver\Media Center 33\Library Backups\backup.zip).
Copy that backup.zip file to the Desktop of the new machine.
Run MC on the new machine, File>Library>Restore (point to the backup.zip you just saved on the Desktop).
Restart MC if needed.