If you press the button and nothing happens here's what you should do. first, confirm the engine is not seized up. pull the plugs and reach down and rotate the motor at the coupler and confirm the motor rotates. if yes, then remove the plugs to the starter button (they are in the rear right near the electrical box) and jump the starter button to confirm the starter switch is not defective. if still nothing open the electrical box and jump the two large leads on the starter selenoid. careful as you will get a spark. if it turns over you have a bad selenoid. if not, then you have a bad connection, wire or starter. the final test for the starter is to use a car jumper cable and jump the positive lead of the battery directly to the positive terminal of the starter. if nothing then you have a bad starter.
As you can see by these steps you are eliminating each part in the starting chain from the easiest to access down to the hardest.