Target start the problem child and leave connected to the working machine.

When you choose "install mac OS X" on the CD/DVD in the working mack it will reboot to the installer.

Before you actually complete the install you'll have to walk through the installation one step at a time and at some point the installer will recognise you have a working system and ask you what volume you want your install to be on, and what type of install you want to do. Choose clean install and target the firewire drive.

You're good to go from there.

N.