Small Engine Troubleshooting Problems? Ask a Mechanic Now.
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So the engine dies when you try to either move the control levers from neutral or brake position as well as if you engage the mower deck.
This sounds like a seat safety switch issue, the seat safety switch is not telling the rest of the system that you are present in the seat therefore when you try to do either of the two things mentioned it is killing the engine. I would first start by checking the wiring that goes to the seat safety switch to make certain that they are connected properly and that there are no bare spots that could be shorting or grounding out.