No, you don't want to download grub: it's already been installed onto your boot partition, but I suspect the installer hasn't installed it into the MBR correctly. This is a known problem with the FC6 installer. Boot up the CD/DVD in rescue mode ("linux rescue" at the prompt), then follow the prompts, mounting your system under /mnt/sysimage when asked. When you get to a shell, do the following:
Remove the disk and boot normally.
bash# chroot /mnt/sysimage
bash# grub-install /dev/hdb