Taditionally Cub use Yellow wires for the Magneto cut out circuits so unlikley that a detatched yellow wire will prevent the engine cranking.
It may not turn off and if you bought it used and considering the position near the rear axel I would guess it is the reverse cut out wire some one ripped out.
Start at the beginning, the battery.
Check battery voltage between the terminals , the + terminal to engine block and - terminal to + on the solenoid.
They should all be the same +/- 0.5 V and hopefully around 12.5 to 13
Do that and post the results for furthur instruction