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The brake pedal switch only makes sure the brake is in while you are starting the engine. Once it is started the brake switch does not play a roll in the engine running. The safety switch that can shut the engine down when you release the brake is located under the seat. It is there to make sure that you are seated while the engine is running and driving
Check the seat switch and make sure all the wiring is plugged in. If you find everything in tact then you can try to bypass the switch for testing purposes only. First disconnect the switch and try the mower. If that does not yield any results then jump a small wire between the two connections and try again. If you find that the switch is bad then make sure you replace it so that you do not get injured by the mower