The coil is behind the flywheel.
Does the spark plug get wet with gas when you try and start it? If not replace the fuel filter, (probably a screen in the gas tank), and the fuel lines then the carb...
If I'm looking at the right manual from www.toro.com
this unit has a diaphragm type carburetor. Where the fuel line goes on the carb on the other side of the carb you can take the top/bottom off of it either 4 Philips screws or 1 big straight screw in the center, take them off and inspect the diaphragm, the little screen, squirt it all out with carb cleaner.