I downloaded Fedora 7 KDE's live CD from the official website and checked the data integrity of the torrent I downloaded. The torrent was downloaded properly, as KTorrent stated.

I burnt the ISO image using K3b and the data verification was successful.

When I ran the Live CD, I checked again the MD5sum and it was successful.

After all those, when KDM was supposed to come out, my screen just turned black. I rebooted and rebooted and the same thing happened. I even waited for about 10 mins for KDM to come out, but I was stuck with the black screen.

How do I run the Fedora 7 KDE live CD?

Any chance you are having video driver issues? Which videocard have you got?

I have a VIA S3 Unichrome Pro

I seem to recall some people had issues with that one while Fedora was still Fedora Core 6; this may not have been solved yet because Via doesn't appear to open source its drivers.

If you get the blank screen, try hitting ctrl + alt + backspace to see whether you get a command line. If not, you need to reboot and select single user mode.

Whichever works for you, the next step is you to edit xorg.conf from the command line:
Type these commands:
su -
(root password)
vi /etc/X11/xorg.conf
Look for the "Device" section and check which driver is being used. You can substitute it with vesa, which is a universal driver that should be failsafe
press i to enter editing mode
replace driver "(driver)" with "vesa"
press esc to leave editing mode
type :wq to save (+enter); if you made a typo, use :q! instead (this will close xorg.conf without saving anything so you can start over)
You should be back at the command line; type startx (do not reboot - this is OK for a system that was installed to hard disk but not for a liveCD because the cd keeps all changes in RAM - if you reboot, RAM gets cleared and you need to edit xorg.conf again).

isn't there a boot option/parameter for this?

No, unfortunately not. Have you tried my suggestion? If it works, then it may be more convenient to free up some space on your system and do an install, that should save you the chore of re-editing the file everytime your reboot.

Edit: there may be something that will things a bit easier (although it won't be much). If VIA have a Linux driver, you could download that to your hard drive and then install it from there. However, because you're doing everything in RAM, you'll still need to do this again after each reboot.