Why not save the files to removable usb hard drive. Or burn to disk.
------------------------------"To better understand why you need a personal computer, let's take a look at the pathetic mess you call your life."
Reply to badge
If your old computer doesn't have a cd burner and probably no usb connection, you can buy an external usb hdd enclosure, they are quite cheap. Remove the drive from your old computer and fit it in the case, then plug it in your new computer to get the files off.