My iMac G5 has bad motherboard, can't boot, I have ext HD with backup using OSX Tiger, bought mac-mini with Mountain Lion, how xfer files??

All - my 2005 iMac G5 motherboard finally failed (leaking caps) and I can't boot. I just bought a new mac-mini with OSX Mountain Lion. The files on my G5 were backed to an external HD using the Backup software (umbrella icon) that was part of Tiger OSX. All the files on my external HD are just backup files from the Backup software. I didn't copy files to the ext HD directly (I wish I had!). Key Files are MS-Office files, and iTunes. Is there a way to xfer the files to my new mac-mini? Thanks!