Without seeing the motor, it's hard to determine the course of action.

Spraying a penetrating oil onto the valve shaft and guide and gently hitting the valve stem might free it. If not, you have to remove the valve from the head area.

I would worry less about spark damage to the piston, which I don't think would be a problem, and more about the unbalanced power of the motor.

Either way, I don't think it's too big of a job and I would certainly try that before replacing an engine.

First, baymee is correct about the spark action doing no harm to the piston, or any other part of the cylinder.

Tell us what you have done come to the conclusion that a valve is stuck. And whether it is the intake valve or the exhaust valve.

Also, regarding the carbon blacking of the engine and hood, can you tell (or get a general idea) where this carbon/soot is coming from on the engine?

What about the inside surfaces of the air filter, the air filter housing surfaces between the inside of filter and the carburetor throat and on down into the carb and intake manifold? Are any/all of the above surfaces covered with carbon black?

This is in regards to Mownie questions.
I came to the conclusion that the valve is stuck because after running the engine for one hour the right plug is clean and dry in new condition with no sign of an explosion. If gas was getting into the cylinder and the plug was not firing, the plug would be wet with gas and have a gas ordor, this plug is clean and dry and ordor free. The air filter is new and there is no carbon in or around the air filter and carburetor. I don't know where the black carbon is coming from but it only happens when running on one cylinder. I have been told that the cost to fix this problem could be $500 or more,including pickup and delivery, and if this repair is not done correctly, other problems could pop up and cost even more. So it might be to my advantage to put this repare cost to a new tractor and save all this aggravation and cost.

Take the spark plug out of the suspect cylinder. Tie the spark plug wire safely far out of the way. Put your finger tip over the hole and have someone crank the engine. If you have any compression or suction, the valve is at least partially working.

Unless you have a compression release, which I don't know. You can also take off the valve cover and see what's going on.

What baymee said. Take the valve cover off and check the push rod. If it is bent, the valve is stuck closed. If it is straight and won't stay in place the valve is stuck open.