install a fresh Server on your new computer get it up and running. if you are going to operate the server off of a different port than your last server hold off on setting that up. then just replace a few new folders/files with the old ones
Relevant folder/files from old server on Ubuntu are
/etc/default/subsonic
/var/subsonic/db/
/var/subsonic/playlists/
/var/subsonic/subsonic.properties
now your new Server looks just like your old one. Adjust music folders and ports as necessary. I would probably handle port forwarding manually to make sure you deleted the old rule if you are use the same port.