I really just wanted to ask the carb question first and maybe start a thread if the solenoid doesn't solve things. I just got a thin enough wrench to get it off. Before I bought the tractor, I confirmed it would fire on starter fluid and continue to run if given an occasional puff but it wouldn't continue at all without the puffs. I got several people at the store to confirm that they didn't know about any problems other than not starting. I accept that I am taking a risk and even if I get it running, there may be other problems. I will start a thread if it's not the solenoid. Good to know you can't always hear the click. Thanks.
Testing a carb solenoid.
Get a cheap Chinese wrench. Grind the faces down so it will fit to remove said solenoid.
Turn off fuel valve or install one if you don't have one.
Remove solenoid. Watch for a gasket to keep and reinstall.
Key on should RETRACT the plunger tip UP INTO the solenoid body. Key OFF should EXTEND the plunger. Cycle the key numerous times. Make sure wires are connected good to solenoid. Key ON, one wire is battery voltage and other is ground.
OR, if you want trouble free slash never have to worry about THIS part again failing on your and not starting, snip off the plunger. You will have to shut the fuel OFF like 1 minute prior to killing the engine. As in killing the fuel while driving back to the garage.