Hi,
If the Cub is a 1951, it probably has a Battery Ignition unit, not a magneto, but I don't know which it has.
I would test the power of the spark the Battery Ignition unit is making.
Be sure the Cub doesn't roll while doing the spark test.
Remove the ignition wire from the center post on the distributor cap, and hold the wire by the insulation, with the metal end about 1/4" from bare metal of the engine block.
Be sure the transmission is in neutral, turn the ignition switch to on, and run the starter.
The spark should jump the 1/4" gap, and be blue or white. A yellow spark is weak, and needs improving.
The engine may not run, or run right, with a yellow spark.
Do the test in a building, or not in bright light, so you can see the spark well.
The battery should be fully charged for the spark test. Charge the battery if necessary.
A low output charger is better, it may take several hours to charge it.
You said you replaced the points, so there should not be corrosion that can happen with old points.
They have said on here that some new points come with a clear coating on them, to prevent corrosion I guess. Power won't go through the clear coating, it has to be filed off using a point file.
Clean off all filings with a clean rag.
There are pictures of the points and condenser, inside the Battery Ignition unit in the Cub operator's manual. The points need the right gap also, .020" for a Battery Ignition unit.
The condenser or coil may have quit.
It is sort of common for the old original Cub coils to quit. Some of them work when cold, then quit when warm, then work again when the engine is cold.
The ignition timing should be checked with a timing light, the Cub service manual says. Then you know it is right.
The tractor will try to run with the choke all the way closed but as soon as I let off the starter it will not continue to run.
The main jet on the IH carburetor may need cleaning.
The main jet is low on the side of the carburetor, it is the 6 sided brass colored part.
To clean it, shut off the gas, unscrew it from the carb, wash it in solvent, or carb cleaner, then use a small wire in the hole in the end of it, and be sure the hole is open and clean.
Don't use a wire bigger than the hole, or force a wire in it, the hole has to be a certain size.
Wash it after using the wire. It should have a gasket on it.
Don't tighten the jet hard, they can break.
If the gasket is old, it may leak if you reuse it.
TM Tractor Parts has a new gasket for the main jet. They are near the bottom of the Forums page.
Below is a picture of cleaning the main jet.
The 2nd picture, from TM Tractor Parts, shows the engine side of the IH carb, the choke arm should be in this position when the choke valve is fully open, and it has the original length choke rod. Be sure it is tight on the shaft.
