You need to pull the "flywheel" (magneto more accurately??) off and you will see the keyway and the key unless it sticks to the flywheel or falls out upon removal. Larry's suggestion is a good one. The Woodruff style key used is very soft, similar to a shear pin on an outboard, and serving the same purpose.
Lawnmowers, and small engines in general, can be very frustrating especially to those of us that fancy ourselves to be pretty good mechanics based on our successes with automobiles.