I have solved this problem thanks to an excellent tutorial that I've found on FedoraForum.org:
Now GRUB works fine and I have the dual-boot system that I need. By the way, after playing with it for several hours, I have to say Fedora Core 6 is absolutely wonderful. However, I can't understand why this odd installation problem with GRUB happens...
Thanks Werner for the suggestion on removing the Windows hard disk. I was about to try that when I found the tutorial above.
k61824, I'm pretty sure you can fix this problem in the same way.
In case somebody is interested, if you need to access the Windows NTFS volume from Fedora, as is my case, FC6 doesn't have core NTFS support. However, it's very easy to add this functionality with the ntfs-3g driver. To install it:
yum install ntfs-3g (as root)
for usage instructions.
Juan Conejero, Pleiades Software