Yes, connections, solenoids and starters could cause this problem, and if you don't want to check the valve clearances then you can start replacing each one of these parts. Sorry, that's about all I can help you with. Bye.
I haven't tried jumping the tractor off of a car. Like I mentioned on my first post, if I charge the battery up to ~13.5 volts then the tractor starts up fine. I do notice that the engine turns over faster than it does at 12.6 volts. It may be due to the compression release not working right as some have mentioned - if so then I guess the higher voltage to the starter overcomes the failure of the compression relief to release pressure.
But back to my original question - could a bad connection, bad starter solenoid, or weak starter not also cause this problem. Do starters ever weaken over time? Just trying to consider all possibilities.
Sorry Rivets - didn't mean to offend. I had such "tunnel vision" that it must be an electrical problem that I couldn't fathom that a valve clearance problem might be the cause of my problems. I have watched some really good videos on YouTube that show how to adjust the valves on a B & S engine. It looks pretty simple so I think I'll give it a try. One guy on a video said that you really need to check the valve clearance on a B & S engine yearly because they can come out of adjustment. If the valve clearance adjustment doesn't fix the problem then I will start troubleshooting the starting system.