The things that can cause the tractor to make no sound when you turn the ignition switch to start are:
The ignition switch
The clutch/brake safety switch
The attachment clutch safety switch
The starter solenoid
The wiring in the start circuit
Make a jumper wire from number 14 or 12 wire about 4 feet long. Strip 1/2 inch insulation from both ends. Remember the wire in your hand is hot and will arc if it touches any part of the engine or tractor.
Put the tractor in neutral, put the emergency brake on, disengage the deck, and turn the ignition key to on.
Touch one end of the jumper to the positive terminal of the battery. Touch the other end to the white wire on the starter solenoid. The starter should turn the engine over and the engine should start. If nothing happens the battery is probably dead. Have the battery tested.
If the engine starts, or turns over, go to the attachment clutch switch which is behind the dash on the bracket for the deck engagement lever. Remove the plug from the switch with the 2 white wires in it. Touch the jumper to each wire. One wire won't do anything, the other should make the engine turn over. If the engine doesn't turn over the white wire is broken between this plug and the starter solenoid.
If the engine turns over install the plug back on the switch and go to the clutch/brake switch underneath the tractor near the clutch/brake arm so that it activates the switch. Remove the white wire plug from this switch and touch each wire. One wire should do nothing, the other wire should make the engine turn over. If it doesn't the attachment clutch switch is bad, replace it.
If the engine does turn over, install the plug back on the switch and go to the ignition switch. Pull the connector from the back of the ignition switch and touch the jumper to the white wire in the connector. If the engine doesn't turn over the clutch/brake switch is bad. Replace it.
If the engine does turn over the ignition switch is bad. Replace it.