Small Engines (Lawn Mowers, etc.): key start on 12hp snapper, correct switch, key switch

Question
I have 3 wires that when connected where the picture shows the mower does not start with the recooil rope or the key when I diconnect one wire which is brown I can only start with the recoil rope  

Answer
Not sure I am clear on your question but it sounds like you have either the incorrect key switch or it is wired to the incorrect terminals (because disconnecting brown wire) allows the engine to have spark.  This means the key switch is grounding the ignition out when it is in the "on" position.  You will need to verify you have the correct switch and the colour coding of the wires (and the circuits) matches the diagram you are working from.  Hope this helps.