" It won't start " meaning "it won't turn over", is that the reason you did replaced the ignition switch ? YES,
First, check the battery and starter cables for their tightness or free of corrosion and physical damaged.
See this Starting system simplified diagram. Have a help from an assistant to crank the engine, use a 12 volt light tester or a digital voltmeter, apply it to the starter control circuit.
If there isn't no light or no volts, then the ignition switch is the culprit.
If there is light or 12 volts and the starter isn't cranking, then the starter is the culprit. Have the starter to bench test for free at the local auto parts stores.
Note: a 3/4 charge battery is 12.50 volts
A discharge battery is 11.75 volts.
A battery under a cranking load and it is reading less than 7 volts,it will be a recycled ( junk ) battery.