Generally, you use a Linux system's Live CD to retrieve files and even repair a broken system; however, I had lost Fedora's Live CD. So instead, I used Ubuntu Linux 10.04's Live CD, which I found in my collection of Live CDs. I inserted the disk, rebooted the computer, and came upon the Live CD's instance of the GNOME desktop environment. The hard drive was listed as a readable entity, but when I clicked on it, I got an error message saying that the disk could not be read (a very indescript message, yes).
I fumbled through my disks and found a fairly old openSUSE 11.2 Live CD. I was really excited, because openSUSE has an automated system repair program on it. It was sure to figure out what was wrong. Well, wrong. It could not read the disk, and it seems that means it cannot help at all. How disappointing.
Searching through the disks again, I came upon an Arch Linux Live CD (yes, I have a lot of Live CDs). I booted it up and came upon the infamous command-line. I tried to mount the hard drive with
mkdir /mnt/hd; mount /dev/sda3 /mnt/hd, and it said it could not recognize the filesystem.
I finally knuckled down and burnt another Fedora Live CD, and guess what? I was able to read off the hard drive no problems at all! I was able to retrieve my files. What did Fedora do to make it so that no other Linux could read its filesystem? What? I still do not know, but I do know that openSUSE never had that problem, so I installed that instead.
The moral of the story is that if you want to retrieve your files from a Linux, you should probably use that distribution's Live CD.