PTO switch or lever left "engaged" perhaps?
Many tractors are interlocked to inhibit starter operation if PTO is on.

I may have turned off the engine before disengaging the PTO and blade deck levers but I disengaged before trying to start again.

OK, at least we can eliminate that.
What about the battery? Is this an old battery? How old?
Did you have to charge it before you got it started the first time? Do you have a volt meter (hand held test meter)? If so, what is the voltage reading of the battery now?

I think the battery is only a year old, maybe two. I was surprised I had such an easy time starting it the first time for the season without having to charge the battery, before I turned it off and it wouldn't turn over.

The voltmeter on the tractor reads 8 (lowest number on the meter) when off, 13 when I turn the key to run, and 8 when I turn it further to start.

My battery charger says the battery has 12.3 volts, and the alternator check function on my battery charger says "Fault". Does this mean it's the alternator, or just that it's not the battery?

Thanks!

The readings that you see, do change when you turn the key to "Start" position. Best way is to take the battery to somebody who can check it without trying to sell you a new one. A "Load test" is a good thing to try.
If the engine is Overhead valve type, maybe a valve adjustment is in order. If you do a lot of stopping and starting, the battery, if more then two years old, might not be up to the starting job. And, if you are handy with jumper cables, use them to connect to a known good battery, but be caareful around these modern cars and trucks, necause an unintential GOOF can cost you lots of cash!!
I have used battery jumper cables, from my truck, to the mower battery connections, then started it that way.

The "simplistic" alternator check function on most consumer grade battery chargers will not recognize the weak output of some small engines.
Best to carry that battery (fully charged) to an auto shop or parts house and let them load test it.
Testing the output of the engine's charging system can be done easy enough, once you get the engine started.
12.3 volts IS NOT a good reading to have. Ideally it should be 13.2, or even 13.6.
Once you get the engine running, with the engine running at wide open throttle, a volt meter should register about 14.2 or 14.4 volts, after it has run at that speed for a few minutes (to put back what was sucked out by the starter).
If your system voltage DOES NOT reach 14 volts, you have a charging problem.
We can cross that bridge when we get there.

Thanks for all the info guys,

Fortunately my spare lawnmower started so I could at least cut the lawn before heading out of town. We'll try the load test on the Wheel Horse battery when I get back.

Thanks again!

The 312 almost certainly has the cast iron Kohler with compression release, but still a flathead. I doubt engine trouble in this case.

Sounds like a safety switch to me.

Hi guys,

I'm back. After taking the battery to a parts store, I was told the battery is 6 years old so I bought a new one, installed it and no change - the engine doesn't turn over but the lights work.

As for Baymee's safety switch theory, when I'm sitting in the seat, the seat warning light is off, and when I press on the clutch to start, the clutch warning light is off. The PTO clutch warning light is off as well. All my warning lights are off.

I've noticed however when I turn the key to the run position, I hear a faint ticking sound about every half second like a bomb. It continues for about 20 seconds after I pull the key out....

Any ideas?

Thanks

Sounds like the starter solenoid might be going. perhaps a starter shop may look at it or... a light tap with a hammer may work it free.

Does the starter solenoid CLICK?