Have you checked for spark with spark plug removed, holding the high tension wire close to a grounded metal part of the mower, with the controls in the start position? (If you prefer, connect a good spark plug to the HT wire and ground the body of the spark plug.) If you have done this, and found there is no spark when you spin the engine, then there is a magneto problem. There are three areas to check next: that the high tension lead is in good condition (not broken or grounded); that the magneto is the correct distance (0.5 mm) from the outside of the flywheel; and that the kill switch and its wire are not grounded. To make that third check, if possible disconnect the kill wire from the kill switch, and ensure that there is no point along that wire where it has cut through its insulation and become grounded. There are only two wires coming out of the magneto: the high tension lead to the spark plug, and the kill wire.
If the kill wire is not becoming grounded (either due to a defective kill switch or a fault in the wire's insulation), the HT lead is OK, and the magneto is the correct distance from the flywheel, it looks as if your ignition module is misbehaving.
