Have you tried a simple portable mini drive??
These are small, USB devices that you simply plug into your computer, download or upload the files you want to move to another computer. They come in various "sizes" from 256 megs all the way up to 4 gigs!
They are tiny also...they simply look like small "sticks", for lack of a better description.
Just ask in any electronics store for "thumb drives" or, as they are sometimes called, mini storage drives. Memorex, Sandisk, Pny, etc. are all brands that are out there on the market.
They are simply wonderful for moving files and for easy backups as well.
Hope that helps!