So you have tried to repair the G5 hard drive by using the Disk Utility from your PowerBook while the G5 was in target disk mode and it could not repair the drive?
If the Disk Utility is able to repair your drive but you still cannot boot from it, you can just reinstall Mac OS X using "Archive and Install". No need to copy all the files over to the powerbook.
If Disk Utility cannot repair the G5 hard drive, then you should copy all important files to your external drive or the PowerBook hard drive. Don't zip them - the zip file would be created on the damaged disk and this could cause more damage.
By the way, if you connect the external drive to your G5 and then put the G5 into Firewire target disk mode and connect it to your Powerbook using another Firewire port on your G5, the PowerBook will see both the internal drive of the G5 and the external drive connected to the G5.