Hi,
Here is info for doing a compression test, if you need it.
Open the throttle fully to do the compression test, so the engine can get air.
Have all 4 spark plugs out of the engine at the same time.
Charge the battery fully before the test, and use the starter.
Charge a new battery also, they are not always fully charged, a low output charger is better, 6 amps or so, that automatically goes down as the battery charges. It may take several hours to charge.
The Cub service manual says a Cub engine before Cub serial number 192113 has 107 lbs of compression, when turning at 240 RPM. That is probably for a new engine.
Some less is ok, they have said on here 90 lbs or above is ok.
I would test the power of the spark the magneto is making.
Be sure the Cub doesn't roll while doing the spark test.
Remove the ignition wire from the center post on the magneto 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.
They have said on here that some new points have a clear coating on them, power won't go through the coating, it has to be removed by filing the points. Wipe off all filing with a clean rag.
The magneto timing is important, the engine can start hard, or not have as much power as it should if the timing is wrong. Below is a page from the 1949 Cub owner's manual telling how to time the magneto.
There are pictures of the points and condenser, in the Cub owner's manual.
The coil may have quit, or partially 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.
TM Tractor Parts has a new magneto coil, below is the listing, you can look at the pictures.
http://www.tmtractor.com/new/el/713fp.htm
Below are their listings for a new rotor, and rotor drive gear, you can look at the pics of the gear teeth.
http://www.tmtractor.com/new/el/294fp.htm