I'm running from that livecd right now.... thought about the PCC hardware listing.... I'm attaching those screens. The livecd finds the controller.... do I need to modify some of the settings? Why does it say IDE under the SATA controller? Maybe some setting on the drives (but then why does my prior install find them?)?
I see two possibilities, bad burn or bad read. If the burn checks out, the read lens may be dirty or misaligned. I'd go with dirty first.
Have you tried the disk in any other computer?
My last motherboard, had to have RAID turned on, AHCI turned on, then JBOD selected, in order to see individual SATA disks. I would suspect the BIOS settings, except the other installation is working with the current BIOS settings. This is why I'm thinking dirty lens or dying optical drive, if the disk itself checks out. I've personally never seen a properly burned disk have fdisk -l fail to see the drive partition tables when the proper modules are loaded. and they do seem to be loading in your tests.