Unless you're doing things with your firmware options that you've not described, the inconsistency of the appearance/non-appearance of the option to add boot options is troubling. This sounds more like a hard disk issue, though, almost as if your hard disk connector were flaky. If that were the case, though, I'd expect there to have been major problems when transferring files during Fedora installation.
You could try booting with the rEFInd boot CD (see here
for a download link) and see if that produces anything. Also, most computers have some way to reach a boot device menu, typically by pressing F2, F10, or F12 during the boot process (but details are annoyingly inconsistent). See if you can get such a menu, particularly if the rEFInd CD doesn't boot for you -- you might need to play with the options to boot the CD in EFI mode vs. BIOS mode.