well first lets see if it has spark.
If you have an carburetor cleaner (that is NOT non-flammable) and/ or starting fluid, or even a bit of gasoline, sprayed right into the carb for about a 2 second burst should be enough for it fire up, so spray a starting fluid into the carb, try to start, if it runs then dies, fuel delivery issue, either the carb still needs cleaned or the gas is bad/ water contaminated.
however this one is a choke version, not primer type.
now if it doesn't start at all, i would be looking for spark...remove the top engine cover (3 10mm screws) you'll see the ignition coil, and a small black wire going to the back of the engine, unplug that wire, it is the Kill wire.
try to start with that wire unplugged, repeat the earlier steps, and if it starts with the wire unplugged, there is an issue with the kill/brake assembly at the back of the engine or the wire insulation is rubbed off and shorting to ground (mower)
if it still doesn't start with the wire unplugged, bad coil.
** however i
wouldn't mess with over sizing that jet