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.

Seat switch connector has a built in "shorting bar" which will close the kill circuit when the connector is unplugged from the switch. Unplugging the connector from the switch gives the same results as if the seat is not occupied. Seat switch is just one switch in the safety interlock circuitry that can cause the engine to have no spark. The brake pedal interlock switch is actually 2 switches in one assembly. One of the brake switches is dedicated to starter inhibition, and the other switch is to kill spark and stop the engine. The PTO switch also has a circuit dedicated to the kill wire. You can disconnect the kill wire from the magneto to see if that restores spark. If doing that restores spark, something is grounding the kill wire somewhere. Could be a chafed wire.

A couple possibilities. That's a Briggs OHV engine. IF the valves get out of adjustment, the compression release doesn't function. OR, you simply have a bad connection in the cranking circuit. Clean the ends of all battery cables. make sure engine mounting bolts are tight. The ground side is just as important as the "hot" side. Then there's the possibility your battery has reached the end of its life. Charge & get it load tested to be sure. A bad solenoid is also a possibility. This post was edited by bill_kapaun on Sat, Nov 8, 14 at 22:34

I would check all electrical connections starting first with the battery. Remove and check fluid(if not sealed battery and replenish fluid with only distilled drinking water)and put battery on a charger, unless you find battery is bad, while doing these next routine maintenance procedures, start with spraying the ignition switch with some WD-40 and just putting in key and turning on and off for at least 30 seconds to get rid of any electrical contact corrosion, then move on to the back side of ignition switch and pull off all electrical wires(remember to do this 1 plug at a time to not get wires messed up) and clean any corrosion that may of built up over the years and put on some dialectrical grease to keep moisture away. Next move to the starter solenoid and clean up all the wires there and move on to the starter wires on starter motor. What you're doing is looking for, brushing off and cleaning up, any corrosion on these wires, and to check on if there's any weak links in the electrical system and either repair or replace any wires or connectors if needed. If you do find corrosion, especially with the larger starter cables, remove them and neutralize the acids with baking soda and water mixture. If too far gone, just replace. After all this, then move on to checking spark plugs and with them being so cheap, I would just replace(don't forget to check on the air gap--don't trust factory). Clean up/replace air filter if needed and do the same with the fuel filter. These procedures will get you more into the habit of doing a process of elimination and finding and correcting future problems and saving money than taking your mower to a repair shop.