Do you have another computer? If so go to here: http://partedmagic.com/doku.php
, download the version that best fits your hardware (the i686 works for most modern hardware, but if you have a 64bit cpu, then the "x86_64" version might be better). Burn it to a CD and boot your machine from the CD. The disc has some nifty tools for working with broken machines. I use for everything, including rescuing Windows PC's. If you can boot off your Fedora disc, you could use that instead.
Either way, you just need to mount the internal hard drive, plug in you USB drive and you should be able to copy any data you need.
You could do this from the DOS screen, but that is much more complicated if you don't have any experience with the Linux terminal. I would go the PartedMagic CD route first.