I take it that the engine does not even TRY to start, but just spins when the starter is engaged. You need to make the test that mownie suggested. There are probably more safety interlocks than just the seat switch, and one of them could be "shorting" out the system. There is likely one on the clutch/brake pedal, and another on the PTO lever (the one that engages the blades), and one on the shift mechanism (to prevent starting if the transmission is in gear.) Testing these will require a multimeter. There is also a ground wire from the engine to the frame; typically on Husqvarna/AYP/Electrolux/Roper machines, it is a rather small black wire that is attached to the underside of the tractor frame just below the engine and inside the right front wheel. You've likely got a bad magneto or (more likely) either an electrical short caused by chafed insulation, corrosion, or loose connection, or a malfunctioning safety interlock switch. This all based on your being certain that there is no spark at the plug.

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.

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.

Yes, you will probably have to prime it especially if it's the cheap vacuum plastic pumps until the gas get pulled through the fuel pump and carb. While you have them plugs out attach them to the plug wire or wires and ground out against the head crank it and look for spark??? do you have spark?? hopefully the answer is YES. OK, on down and one to go. Now squirt some carb. cleaner into the spark plug hole a two to three second blast is usually enough. put the plugs back in, connect the plug wires lift the throttle up and crank it, it should fire off the carb. cleaner for 4 or 5 seconds. If it does and it dies out. squirt some down the carb. and crank it. should stay running after two or three times. Carb cleaner will NOT hurt your engine. IMO it's better than raw gas or starting fluid. Why raw gas it a fire hazzard waiting to burn you or your mower up by spills. Starting fluid washes all the oil out of the comb chamber and has NO lubricating abiliity. Carb cleaner evaporates quickly and is in mist or spary form. has lubricating ability. Course all of this is MY opinion....Others may and do dissagree. Don't hit a lick, then you may want to revaluate you valve installation procedure and adjustment or do a compression check and see if it's got any compression