You can't reinstall the System if you are booted from the disk you are trying to install on. You have to be booted either from the install disk or from another bootable disk.
When you hold the C key down it should boot into the install disk (provided it's the one that came with your Mac or is a retail Snow Leopard disk - if you are trying to boot from an install disk that came bundled with another Mac it may not work, though you should get an error message, and you won't be able to install anyway.
Holding the option key should bring up the startup manager, which shows you icons for the available boot disks - in this case the internal disk and the installer disk.
If your Mac is simply ignoring the instruction to boot from the correct disk then the CD drive may be faulty. Try testing whether you can mount some other CD in it.