I would start with the switch. Pull it out and test it if you have a DVOM. you should have continuity between the B terminal and the S terminals only when the key is turned to the start position. If you don't have a DVOM, usually a NAPA auto parts can test the switch functions for you, and they can probably also sell you a new switch (i needed) for far less than it will cost from Argo.
A well regulated Militia, being necessary to the security of a free State, the right of the people to keep and bear Arms, shall not be infringed.