Ouch! That hurts!
First, in Linux, the directory slashes lean the other way. ;)
Am thinking that what you have will work on 15.04 and it's probably advisable as 14.10 has reached end of life, has it not?
So install a fresh 15.04 first and get the parts that make Moodle go installed ... php, mysql, apache and running first.
On the DB step ... I'd shut down the mysqld on the new server before copying the raw moodle DB files to new server.
From the /var/lib/mysql backup you have only the 'moodle' directory contains the DB files you need. The others should be already be created on the new server by that environment. The moodle directory and files contained therein needs to have the same ownerships/permissions as you see the other newly created directories/files ... say the 'mysql' ... on the new server. *** I'd also run mysql_upgrade as your moodle DB from old server might not be the same MySQL version as on new.
You could copy the php.ini, apache.conf, mysql.cnf files to new server, but I wouldn't use them ... use them only for reference the tweaks you might have added to them. Let new server gen those.
The other directories you have 'moodle' is the code and could be placed in apache root. moodledata in the same location on new server as on old. Ownerships and permissions would have to be reset as the method you use to copy to new server will probably tag all files/folders as root user.
Check the config.php file of the moodle code and make appropriate changes.
Once you get everything in place ... mysqld restarted ... mysql_upgrade run, tweaks to PHP and Apache made and apache started ,etc. then check via browser of another workstation.
Oh, yeah ... DNS changes. Don't forget that. The new server should use the same FQDN as the old server so you don't have to search/replace all the URL's in the Moodle that had entries in the DB pointed to the FQDN.
Best of luck!!!
'spirit of sharing', Ken