If your OS folder has corrupt files, you will be unable to boot into safe mode. The most easiest way to back up files to an external hard drive while your main OS is down is to use a Live Cd. A live CD is a OS that can be booted up via a disk drive. I use Ubuntu but you can use any one. They are primarily free of charge and all you need to do to boot them up is to change your bios settings to read the CD drive and it'll automatically boot into it. If the hard drive itself isn't corrupt, you can still access your main drive via the Live CD but you may need to force mount the hard drive because it is highly likely the Live CD will not automatically mount your windows drives. Most likely programs, will not be preserved but there maybe a way to do it via a Live CD. I just do not know of one.
If the files are inside a partition that's separate from the main partition, you do not need to move them. You can just reformat the main partition alone and do a fresh install in that partition. But you may move the files in the separate paritions if you have no idea what you are doing and is scared make mistakes.