I think I found the problem. I took the old 640GB Western Digital Drive out of the G5, put it into my Mac Pro and installed the OS onto it, but the system won't boot off this drive. I think the drive is going bad, which is what has caused so much grief with the G5.
Looking around the inter webs, apparently the old SATA-I controller on the G5 can handle a maximum of 2TB, so it is time to buy a new drive and try again. Is it worth getting the SSD upgrade for the PowerMac G5? The thing booted pretty darn quickly on OSX Tiger before the HDD started going bad.