I told one of my friends that I wanted to try a Linux distro the other day and he burned me a copy of FedoraCore 3. Is there any way I can try it out on my computer without fully installing it? Will I still have all of my files if I install it? Can I still run any of my other programs if I install it?

If you just want to TRY linux, your best bet is to download and burn a copy of Knoppix. No install necessary, and it gets you a nice feel for it.

As for anything else ... no your files won't be there, and no you can't run a damn thing. (after installation I mean)

http://www.knoppix.org/
http://slax.linux-live.org/

you could try making a linux partition with partition magic if you wanted, atleast then you wouldn't lose your current stuff. but knoppix is still the best thing to go for.