I then tried to boot from the OSX DVD that came with my Mac (holding down the "C" key, of course) and got hit with a kernel panic every time!
If booting from the CD that came with your Mac the operating system doesn't work, it may mean you have third party peripherals connected to your Mac that aren't compatible with that operating system. The only thing you should have hooked up to your Mac in that event are:
1. Any display.
2. An Apple wired keyboard.
3. An Apple wired mouse.
4. The original graphics card.
In event that's all you have hooked up, you have a hardware issue, and no Snow Leopard didn't cause it. Hardware can not be impacted by Software. However, it may be more sensitive to changes.
You may need to replace the RAM in your machine.
Sometimes 'C' key booting doesn't work, but using the startup manager will:
http://support.apple.com/kb/HT1310?viewlocale=en_US
That may also allow you to run the hardware test, to discover if some hardware is not working right anymore.