Try to install again after checking the media you burned for errors (it's one of the first options when you begin an install).
When you install, make notes about what exactly you are choosing to install and how you are partitioning your drive. Make sure you have more than enough free space after your install to run.
Choose 1024 mb instead of 1000. Red Hat (I'm speaking from personal experience only) can be kind of temperamental about installs, and they say double the amount of ram you have to get the swap.
If you get the same error message, write down exactly what it says. Then do a google search and/or look at the redhat bugzilla site to try to find a matching bug.
If you don't find one, file a report and come back here.
I've never installed fedora, but I have installed red hat 8 and 9 quite a few times, and gotten errors.