If the broken Mac won't run, you'll have to pull the drive and mount it in a Firewire or USB external case. Then, presuming that the drive is good, you should be able to get all the files from it. If it's just the screen on the Mac that's bad and it has Firewire (and isn't really old), you may still be able to start it up in
Target Disk Mode and get it to mount the drive on your other Mac.
Message was edited by: Dave Sawyer