Ignoring issues like getting the new system to boot, a simple way to duplicate a system through a LAN is by using rsync.
There are lots of ways to do it, but a simple one is to (1) boot both systems using the latest Knoppix CD, (2) mount the old filesystems, (3) mount the new filesystems, (4) start ssh on both ends, (5) change the receiving end Knoppix root password (i.e., so that you know what it is) and (6) start the rsync transfer. Obviously, you need to manually set up/format the filesystems on the receiving end beforehand.
Code:
rsync -aH --delete --exclude 'lost+found/' /mnt/oldsystem.../ ip_address:/mnt/newsystem...
It would be a good idea to build initrd images for the new system before you do the transfer, but you can always do that from rescue mode after the transfer.