I somehow edited some sentences from my above post. I'll try again. cecr, download the PDF manual as suggested by Bill. Look at the schematic. As Bill said, try "jumping" from the battery positive cable on the solenoid to the small terminal (WHITE wire post). If this makes the solenoid engage and motorize the starter, there is nothing amiss with these 2 items and the defect is "upstream". Using a 12 volt test light or a multimeter (set to DC volts scale) check for voltage at the B terminal on ignition switch. If you do not show voltage on B terminal, the problem is in the wiring between B terminal and the battery. If you do have voltage present on the B terminal of switch go to the next step. Check for voltage at the white wire on ignition switch WHILE the switch is turned to the start position. If you have no voltage on the white wire (while in start position) the ignition switch is defective. If you have voltage present on the white wire (in start position), the ignition switch is good. Next you need to find the clutch/brake safety switch. Beware that in the process of performing any of these tests, your movement of the wire connectors could restore a loose fitting connection and suddenly cause the starter to begin turning. The clutch/brake pedal must be pushed down completely and locked before doing the testing. While holding the ignition switch in the start position, check for voltage on the 2 white wires of the clutch/brake switch. If the switch is defective (or not being properly actuated) you will have voltage present at only one white wire. If the switch is not mounted securely in its fixture, or has become "out of adjustment", it might act like it's defective also. Be sure that the switch is secured properly. If you find the switch is properly mounted and voltage is present at BOTH white wires, the defect is in the wiring or connectors somewhere between the clutch/brake switch and the small white wire post on the solenoid.

This problem could be all the things mentioned by the others. Here is another idea that was not mentioned. I have experienced the same problem and the solution was very simple. When the key is turned to the crank position, battery voltage is sent to positive spade on the starter relay. A common wire (ground) is connected to the second spade on the starter relay. On many of the Craftsman riders, this common wire is connected to the frame with a sheet metal bolt located over the right rear tire. I have found secure bolts holding the wire tight, but no connectivity. If this is the case, find the wire, wiggle the bolt with a wrench and tighten down.

Did the engine seize abruptly? IF so, possible sheared flywheel key. You might want to remove the valve cover and make sure the valves are cycling fully. Running low on oil may have wiped out the cam lobes??

With the new solenoid and a new key switch that pretty much leaves the PTO switch and the brake/clutch switch to test. You can test the white wires at the clutch/brake switch for the presence of 12 volts while the key is held in the start position and the PTO switch is in the engaged (blades ON) position and the clutch.brake pedal in the up position. With the PTO switch and the brake/clutch switch set as described...........only one white wire at the brake/clutch switch should be showing 12 volts (while key is in start position). If you do have 12 volts on 1 white wire at clutch/brake switch, press and hold the brake/clutch pedal down and check the other white wire for 12 volts. If no 12 volts, clutch/brake switch is defective. If you do have 12 volts on both white wires, the trouble is in the wiring that leads from the clutch/brake switch to the starter solenoid. If neither white wire at clutch/brake switch is showing 12 volts, you need to back track to the PTO switch and check the white wires on it. At the PTO switch, with the key in the start position, and PTO switch engaged as before, BOTH white wires should show 12 volts. If only 1 white wire shows 12 volts, defective PTO switch. If neither white wire on PTO switch shows 12 volts, the trouble is in the white wire between the key switch and the PTO switch.