Got to say this is weird. In the initrd image, there is a mini file system with directories and such, containing temporary init files which is supposed to allow the system to run until the / partition gets mounted, including the code that controls that mount, and the rest of the system loads from what's on the / partition. Your error is saying there is no /dev/root and later;
switchroot: /dev does not exist in new root
I'm wondering if there's a problem with the actual liveCD, in that either the installation, or the initrd image, seems a bit short on copied files, at least according to the error messages. It could be file corruption during the installation, or a problem with the disk itself, possibly from burning at too high a speed.
Put the liveCD disk in the tray, reboot, and when the menu appears, use the down arrow key on the keyboard to move down, select the Media Check, and press the Enter key. We need to know if there's any corruption to the disk, first, before trying any reinstallation attempts.
Post your results.