So I took off the starter, opened it up, it looked fine, put it back together, and it bench tested it...where it spun up fine. I greased the gear-pinion assembly up good, put it back on the tractor, and she started right up. My guess is the the gear-pinion assembly was just sticking. I should've tried bench testing the starter before I took it apart though...just so I'd know if it was the gear-pinion sticking or if the starter was just bound (or something along those lines). I'm guessing it was the gear-pinion... Thanks for the suggestions...I'm sure I could still use a valve adjustment.

geu1918, I think walt wanted the engine number and you gave the mower number. Other than that, The starter solinoid has been a problem for me on many vehicles (tractors, mowers, cars, etc). I also had a safety switch go bad, preventing the solinoid from being activated. If you happen to have jumper cables, they could be used to provide power from battery around the solinoid and direct to the starter if desired. BTW, I have seen two types of solinoids. one with 3 wires and one with 4 wires. Both have a large wire from the battery and another large wire to the starter. then a small wire (to the coil in the solinoid) that provides power to make the solinoid click. the fourth wire provides the ground (frame) path for the coil when such connection isn't done inside the solinoid. The ones that have failed for me have had the connection for the heavy wires fail to make contact, even though they still click. Safety switches will exist in the small wires ( ie. the energising or coil circuit) of the solinoid. JerryO

Just wanted to post a follow up on the status of my tractor.. I got a replacement coil as was suggested and I did get a spark and finally got the tractor started again! Just wanted to say thanks to those who posted, especially mownie for providing the B&S site as the part listed on the Sears site was in fact different than what was on the B&S site. It did take a few more cranks than usual and had to take it out of choke to actually get it started, but I'm in business again just in time to get the final mowing of the leaves in! I'll keep an eye on the current situation of it not being able to start while in choke mode, but hopefully that's just because it hasn't been started in so long. If you have any immediate suggestions as to what the cause may be, feel free to post. Thanks again!

if this has an electric clutch, turn it off. Here is another idea to add to those of Exmar. the starter solenoid has a positive wire to the solenoid and a ground wire out of the solenoid. On many of the craftsman mower, the ground wire is attached to the frame at a location over the right rear tire. I have found several with a secure wire, but no continuity. Use a wrench to wiggle the securing bolt. See what happens.