The starter motor draws more current (amps) than the ignition switch can handle - so the ignition switch operates a starter relay that delivers power to activate the starter and turn the engine over.
Follow the fat red cable from the battery to the starter relay and then to the starter itself. There will also be a smaller wire from the ignition switch.
Check the integrity of the connections and the earth return of the relay and the starter.
If they're all good then listen for the click of the starter relay - if you hear the click begin to suspect the starter itself.
Good luck...
Peccavi, June 2013