An external hard drive, with a FAT partition, may well be an option, as long as no file is 4 gig or larger.

Alternately you might want to burn files to disc, but that involves either having multiple optical drives or some way to boot Knoppix and still leave the optical disc free. The toram option may work, but that involves having the CD version and enough memory to hold the entire CD in RAM. Alternately you might boot from an ISO on the hard disk. Or you might hust bypass The need for lots of memory by booting a smaller distro "toram" such as PuppyLinux.

You could e-mail yourself files. That can be slow since it's done at Internet connect speeds rather than local network speeds, but it would get you a copy and if you use a service like Gmail even provide a good backup of the files.

And of course you might consider building a network. If you're lacking a second computer just ask around, many people (including myself) would be glad to find homes for older systems and someone may give you a system that would be fine for network file service for free. If you don't have a router to easily set up a local network, well shame on you. These devices are very cheap and extremely important for safely connecting to the Internet.

Good luck.