Vista has died. Need way to backup files.

Hello, my Windows Vista basic died after it last updated. When i turn it on it gets just before the login screen then restarts to sytem resume. System resume tells me that it cannot fix the problem. I'm assuming that important data is lost. I have downloaded Knoppix (Linux on CD) and can access my hard drive and all my files using this. I would like to back up these files to my external hard and then reboot my computer but cannot. My external will not let me copy files to it. If and how do i make a partition on the external to copy my files, and if i do this, will i be able to copy them back onto my hard drive when i have re-booted it? Is there a better way to do this?.

Thanks, Kel