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.

You might provide the Sears 917.xxxxxx number so one knows WHICH tractor you have. You didn't even mention if it has an electric clutch or manual clutch!

In the owner's manual for this tractor are several items that could be used to check out your transmission function (air purging procedure) and the fender control linkage adjustment. Suggest going thru them in detail. If still no luck, then time to call Sears repair or such. If you need it, a manual can be downloaded from sears parts. Just put in your model number and follow the web page instructions on the r/h side.