As far as the backup is concerned, you could copy the whole of the user\username folder to a safe place. I am assuming you are able to use the OS for that?? If not, get hold of one of the live OS downloads, even Ubuntu, and do it from there.
 
You can then reformat, if the partition table is truly the problem, and do a custom install.
 
More daring. Perhaps you could copy and paste the absent folders from the Windows.old folder? That will only work if the Windows old files are from a previous Windows 7 installation.
 
What happened? Well, I cannot tell you why it suddenly happened. But the Windows.old folder is created uniqely for the possibility of a "rollback", in the event of a failed install. During this process, it wipes the...