If the starter works, which it appears it does, I would agree that the problem must be with the ignition switch as far as I can guess. Not only would it prevent the starter from cranking when you turn the key, but the engine from starting up even if you hot wire the starter.

That is, unless you can get the engine to start and idle by leaving the ignition in the on position when you jump the starter - but I'll assume you tried that.

Do you get power to everything else when you have the ignition on, like CEL for a few seconds, blinkers work, etc?