One of my computers now refuses to boot with the process apparently halting on the line
I understand from a google search that this is probably a kernel panic and a reinstall was recommended. However, the machine won't boot from a CD either, with the same result. It loads an LXF DVD and goes to the boot menu, select the distro to run but then fails.
Does this mean the machine is now unusable? It is pretty old and just used as a printer server to the network. So it's probably due for replacement anyway.
That failure pattern suggests to me that you look hard at the optical drive - looks like it is failing during the reading, and you may need a newer drive (can you boot from an external drive plugged into USB?)