The wires to the carburetor are for stopping the mower, not for running it. The magneto will work with those wires disconnected and flapping in the breeze.
I suggest you remove the spark plug, connect it to the HT wire, ground the metal body of the plug to the cylinder head, and pull the starter. If there is no spark across the plug gap, you either have poor earthing of the ignition module or a failed ignition module.
