Rose, this is a big job with all the parts that have already been replaced. Anyhow, you might start here. " Symptom: Engine will not start
• Disconnect wires at ([C and D] Fig. 51) and attempt an engine start.
If the engine does not start:
• Check the ignition armature (G) for grounds.
If the engine starts and runs:
• Reconnect the wire at (C).
If the engine does not stop:
• Reconnect the wire at (D).
If the engine dies:
• Check the ignition switch ([H] Fig. 51).
Also, remember that the VANGUARD™ series engines are equipped with Oil Gard® low oil protection systems designed to prevent engine damage from running with insufficient oil. This oil float system is mounted inside the engine cylinder. Oil Gard® will shut down a running engine and prevent it from restarting if the oil level becomes too low. When the oil drops below the minimum level, a float pin contacts the sensor mounting bracket in the cylinder. This completes a circuit from the ignition coil, through the module, to the float sensor and then to ground. This grounds the ignition coil and prevents the spark plug from firing. When a restart is attempted, a light in the ON/OFF switch flashes to indicate LOW OI. So, check to make sure you have enough oil. I think the way I would proceed is by just trying to bypass everything ad focus on trying to start the engine. right now it may help to get the owners manual from here and the partslist for the engine from here. Also, take a look at the electrical diagram for your mower.
You do not have to change the switches, just check their function with a multimeter. Hope this helps, good luck.