Suggestions
1)
http://ubuntuforums.org/showthread.php?t=461215 shows that this can happen, when the root file system isn't mountable for some reason. That confirms the theory about CD-ROM driver support, preventing / being mounted.
As he has 2 CDR's if they're both connected, I suggest that you try unplugging the power on one of them (preferably the least important for use later ie. try to boot of CD/DVD RW, disconnect RO drive first. If that fails same, try the other. There's some reason they're not accessible, when the driver in the initrd tries to find them. May be the 1st one, is the one that you're not booting off, making the fetch of '/' fail.
Though it doesn't seem like media errors, I presume you tried "Check CD for defects". According to a LUG master, in another thread, they've seen plenty of problems with DVD-RW drives burning disks that cannot be read properly on target machine. I had a dud myself yesterday, had to redo setting burn speed to 8x, rather than auto.
The Ubuntu GUI crap makes watching the boot process properly off the Live CD more difficult than it needs to be. But hitting CNTRL-ALT-F1 when the splash screen comes, and then being very patient does show something, but I don't think you get that far.
I often find, installs fail on complicated systems with multiple drive controllers and devices. It saves time to strip them down to bare essentials, and then power back on the hardware and configure it, once the basic OS Install is done.
2) Can you burn a Sidux CD ?
http://distrowatch.com/table.php?distribution=sidux (CDRW are fine as KDE-lit version < 650MB). It's based on very recent kernel and Debian "Unstable", it might have driver support that's not in Ubuntu 7.10. It also shows lots of info as it boots up, so you're more likely to gain a clue as to why it's failing.
You can actually if you read the Docs, boot the iso file off harddisk, rather than CDR; you might well find that approach would work. If there's still no joy, then a minimal Debian "Stable" net install, could be done, at least to get info on whether the drives are recognised, and if they are supported.
3) Try Open Suse 10.3
There's more diagnostic messages available, and a failsafe option which doesn't use DMA, which I've used to install on troublesome machines.
As their kernel upgrade to 2.6.22.12 seems to have solved the stability issues, I think it's now good enough to use, but on this board Elandil (IIRC) mentioned that the Live CD is duff. So I'd burn the OS install CD, and you MUST have net connection up to get package updates, or you may have problems booting the system.