OK Johnny,
We are at a point where the potential for going round & round in circles is high because none of us are on the same song sheet.
You are there with the lawnmower that don't go & we are here with information to help but the communications are breaking down.
So let's start with the basics.
On the left side frame rail will be a metal tag with the Cub Cadet full model number
It should start with 13 but in any case, take photo of it and post it so we can show you how to get the correct service manual for your mower , parts book & the same for the engine.
You should have a 16Hp Vanguard twin cylinder engine and on one of the rocker covers will be some numbers should start with a 29 or 30.
IT might also be on a metal tag riveted to the blower housing.
Again we need all the numbers so we can all have the same drawings in front of use either the parts book name or B &S part number or image part number so we all know what is going on.:thumbsup:
"Took the top off the carb " could mean removed the air cleaner base, or removed the upper carburettor body.:confused2:
"Cleaned the carb" can be anything from squirting a couple of shots of carb cleaners down the throat all the way to stripping every part, nut bolt & shaft off the carb and boiling them in an ultrasonic cleaner
And so we all know what you are trying to tell us
Cranks = revolves = spins
Fires = goes bang at least once then stops
Runs = goes bang bang bang for a short while at least.
When not used for some time fuel evaporates inside the carburettor & deposits a gunky varnish that can block off the small passages inside the carb
Heat causes the fuel in the fuel lines to expand and fill the float bowl again which evaporates leaving even more deposits inside the carb.
Water can condense inside the carb which starts corrosion and the corrosion products can block off the internal passages of the carb.
These deposits prevents fuel entering the engine and usually the complete carburettor needs to be removed to clean them out.
As you are not familiar with small engines keep your phone or camera handy & take a photograph every time you remove each item so you will know exactly where it goes back.
This is particularly important with springs & control rods where there are multiple locations for them to go into.