I'm assuming you did check your MD5 checksums, having cleared that....
I had the very same problem you talk about and it turns out it's most probably your cd-rom, check out this link.
http://www.linuxinstall.org/media.php
i actually downloaded all 3 isos twice, even tough the checksums where o.k. the first time and burned 3 copies of fedora. i tought it was a problem with my HD, and so i reinstalled another OS just to check if that worked. and it did, so having ruled out the HD i tried running the test on another computer and voila all three cd's aced the tests.
aparently fedora core 1 gets picky sometimes with cheap cd-rom drives and i know my cd-rom is the cheapest one i could get. and thats only sometimes because i changed cd drives for an ecqually cheap one and it worked out great.
dont try installing if it fails the test, (i tried a couple of times) it's just going to fail again during the install and make you reboot, at best its going to do a very messy grub install that doesnt let you boot up.
