A ) If you plan to restart from new , just install a latest copy of SQL Server Backup onto new server , and re-enter your license key to unlock the program , please stop all databk backup program services on old server or uninstall the program from old server.
B ) If you want to keep old jobs and settings , please do following:
1 . Install latest copy of SQL Server Backup onto new server.
2 . (New Server) Open Control Panel->Administrative Tools->Services , stop all DataBK * service , see following

3 . (New Server) Rename all *.dat files to back them up under installation directory.
4 . Copy all *.dat files from old server to new server
5 . Restart services on new server.
6. Double check all jobs and configration setings , the most important thing is backup devices , if your backup directory is changed , you have to copy existing backups to new directory too.
7 . Do a backup on a demo database on new server , see if everything is ok.