If the shut off wire to the coil is not grounded-(disconnect it and try)then buy a new coil w/ the electronic ignition in it. If yours is old enough to have points- this will give you a much better spark that it ever had. You could also unscrew the starter clutch and check the flywheel key seeing as tho the unit is new to you. A point model won't have spark if the key is sheared. If yours was an electronic ignition model (Magnetron), it is defective if the it won't give you spark. The fix is the same.

Probably the points and condenser. Mine last summer after 34 years of being abused would not fire after being stored outside. It was the points. I have also had the carb off a dozen times to clean it and the tank out and have never replaced one gasket. i have de-carboned the combustion chamber several times also and have used the same head gasket for 34 years. I would do a good clean-up to include the carb. gas tank, combustion chamber and valves (wire brush only using carb cleaner to loosen the carbon with piston to the top and valves closed)(wash out with carb cleaner), fly wheel magnets and coil contact arms, new points, and it should run like new providing it's got compression.