From what little known about purpose of the server, other than your desire to register your site with Moodle Mooch, assume that the machine at the office will be a server and that 'the boss' is all for it ... as well as the IT guys/gals. Moving to a workstation at the office is just a little better than trying to run one from home connection IF the 'office' isn't going to help with it - setting server up with static IP and giving it a fully qualified host.domain name that's in DNS, allowing ports in firewall, etc. :|
Zip the moodle folder, the moodledata folder (recursively - getting all folders files contained therein). (assuming you are Windows based). If linux based at home, tar ball.
A database dump is also needed. Don't know what you have to interact with the DB so following is via command line and really a Ubuntu/Linux thang:
mysldump -u [user] -p[password] [moodleDB] > [moodleDB].sql
Where: [user] is the mysql user that has access rights to export. [password] is the password and [moodleDB] is the name of the database (if you followed instructions for installing Moodle, that's probably 'moodle' as would be the 'moodle' folder at web root and 'moodledata' folder up one level from web root. One does not include the 's above.
Don't have command line mysqldump? Well, then you might have to install phpmyadmin and use it to export the DB to an sql file.
'spirit of sharing', Ken