The new HD is a SATA Seagate Barracuda 1.0 TB, I have no idea if it's 1.5 Gb/s compatible or not. Does that matter?
I did try booting with the alt key to show boot choices and it always indicates there are no options available if the disk is not in the computer. And this is all after the installation process has completed with no errors. At restart it goes back to the initial install screen if the disk is in and the flashing folder (with question mark) if the disk is removed.
Without knowing the series of the drive (7200.11 or something like it) is very difficult to provide a definitive answer, however, I can tell you that some newer Seagate Barracuda SATA drives are probably not going to work, because they require the matherboard to have a speed autonegotiation SATA chip. I think (not 100% sure) these models are not compatible with your PowerMac:
which is exactly what the PowerMac G5 requires in order to properly recognize the hd.
It would be great if you provide us with the exact Seagate HD model number.