Mt Toro 20018 won't start. I cleaned the carburator and now it doesn't even catch at all when I pull the cord.

Check make sure your getting fire to the plug.
Have you hit anything with it.
What made you think you needed to clean carb.

Previously, I cleaned the carb when it started and it didn't catch, but apparently that isn't the problem. It looks like I'm not getting fire to the plug and I tried a new spark plug and it still didn't work. Thank you for the help.

Sounds like the coil..

If I test coil with an ohm meter, would it be no conductivity if it's bad? Thanks.

Hard to get a true reading with an ohms meter.
If you know for sure there's no fire
Replace the coil.