Machine HP A250N
I just had this happen to me a few days ago, I began to boot linux and as soon as I see the message "Setting up file system" cp was executed (which I do not remember telling it to) and began to copy all of my directories until the hard drive would run out of space (12GB with 8GB used), after trying to boot into run-level 1, knoppix and Debian's rescue disk, I was not successful at booting back into linux and maybe fixing any script on inittab or RC.d.
I did mount my partition through knoppix and moved any partimaged scripts in RC0.d through RC6.d, thinking that this might be telling the machine to begin the backup. Unfortunately it did nothing.
I did also studied the possibility to increases my partition by 9GB extra , which I do have available, so that whatever processes was running, would give it enough space to finish the copying. But I do not know how to merge these two partitions.