If your lawnmower fails to start, the most likely cause is ignition failure. Remove the spark plug and reattach the lead. Once this is done, wheel the mower into dark corner of your garage, don a pair of rubber gloves and hold the threads of the plug against the mower's cylinder head. Have a friend crank the engine; if you don't see a bright white spark leap across the plug terminals, test the coil with a volt-ohm meter for a possible loose connection or a faulty coil.
Remove the cowling and fuel tank from the engine by undoing the relevant bolts holding it to the block with a suitable nut driver.
Locate the ignition coil situated on top of the engine beside the flywheel, with its two core ends almost touching the rim of the flywheel.
Adjust a volt-ohm meter to the ohms resistance setting. Touch one of the probes against the metal connector inside the spark plug rubber boot and the other probe against the mower crankcase; you should get a resistance reading of between 0.5 and 1.3 ohms. A zero reading or a reading of infinity means that the coil is faulty and needs to be replaced.
Remove the coil by undoing the securing bolts with a nut driver and unplug the green kill-switch spade connector from the bottom of the coil. Connect the kill-switch wire to a new coil, replace the bolts and snug them down finger tight. Rotate the flywheel until the magnet embedded in its rim is opposite the coil core ends.
Adjust the armature gap clearance by inserting two .01 inch feeler gauges between the rim of the flywheel and the coil armature core ends. Slide the coil assembly forward until the two core-ends rest against the feeler gauges, and tighten the mounting bolts securely.
Clean the spark plug electrodes with a small wire brush and some emery paper and set the gap to .025 inch with the feeler gauge and a pair of needle nose pliers. Insert the plug, tighten it and replace the lead. Remount the cowling and start the mower to ensure that it's working properly.