Sorry for the late response, I only get to work on the lawnmower on weekends. First let me respond to the suggestions above (for which I am grateful, so thank you) and then I will share what my experience lately has been.
To
@Scrubcadet10, thank you - but I’m a newbie and not sure which two ends of the ground cable you’re referring to. The end on my battery is tight and the ground spade connected to the solenoid is tight. I’m fairly sure the other ends of both cables is tight too but I’ll double check tomorrow.
To
@bertsmobile1, thank you - I’m pretty sure the thin wires attached to the spades at the end of the solenoid are correct based on Sears videos and diagrams I’ve looked at. The thin white/power end is on the same side of the solenoid as the thicker red hot wire from the battery. The thin black/ground wire is on the same side as the thicker black wire with a red strip headed to the engine block. I’m sorry, I’m not sure what you meant when you said “jump from the battery cable to the other”, if you could please clarify I’d appreciate it.
@Rusty Knuckles, thank you.
Here’s what I’ve noticed lately with the mower. When it’s “cold” (been sitting), it cranks and fires right up like new. BUT, once I drive it around for a while and use it (I scoop up leaves with it lately), and turn the ignition key off, it will NOT crank or fire again when I turn the ignition key back on. As described above, I get power to the tiny LCD window but nothing else, no sounds, nothing. Like it’s dead. I’ve experienced this “cold start only” phenomenon at least 2-3 times now, consistently. Frustrated and needing to continue my massive leaf job today, I grabbed a screwdriver, turned the key and jumped the solenoid, and it cranked, fired, and started right up. I finished the job by just leaving the mower idling lightly while I emptied my leaf bag instead of turning off the ignition. As a test, once I parked it back in my shed for the day, I turned the ignition off, waited a beat, and tried turning the key again - and again, with the engine ”hot” nothing except the tiny LCD display. I bet if I try to start it tomorrow morning (cold) it might work.
One other thing I’ll mention is that I noticed that the screw holding down the solenoid to the mower frame was a tad loose today and I tightened that, but it didn’t make a difference.
Any clarifications to the questions above are appreciated, and any comments on my experience above are appreciated too. Thank you for your patience with me.