I had this problem this weekend.
It was an MTD. The starter selenoid was bad. There are two switches that have to be made before the mower will start, at least two. One on the lever that shows the position of the deck, and the other is the clutch.
Take a car battery and ground the neg and put the positive on the selenoid battery connection. Try to start the mower.
If it starts, you have bypassed the selenoid. It should run. If it doesn't, you have a switch failure somewhere.