Hum if you are stuck with 56k dial-up only on the first PC,
there would be an easy solution :
from the first PC
sudo dpkg --get-selections > Packages.list

You copy that file *and* your actual /etc/apt/sources.list to
the second computer

Then
sudo dpkg --set-selections < Packages.list
sudo apt-get update
sudo apt-get dselect-upgrade

and the trick is done (provided your second PC has a fast connection)