First do a complete Backup your library. Then download on the computer that does have internet access the last version here:
http://yabb.jriver.com/interact/index.php?topic=75411.0 Download a new install key from JRiver (you'll need this to license the other computer without an internet cxxn.
Copy the three files to your USB flash drive and transfer them to the new PC. Copy your media if needed (preferably to the same drive letter/path as the old PC if possible).
Install the program; click on the install file; then restore your library. If you couldn't use the same paths, you will need to repoint the database (do not use auto import, or you will lose some playback information) -- its part of library tool rename/move -- if you need help on this post back.
Now Make new backups of Library and media
Just in case don't remove everything from the family computer until this worked for you.