Main jet blocked or varnished.

You have spark, fuel and presumably air. Do you have adequate compression? Is the choke fully closing?

Did you open the gas valve?

From your description of the condition of your mower a computer could come up with a bazillion things possibly wrong. I'm sticking to my usual diagnostic method.
..
"I pulled and pulled" Did you pull the rope? Ha, ha. That was a joke.
You have good spark. (I have seen new plugs that would not fire under compression)
. Do you have compression?
If no check for stuck valves.
. Check for clogged or obstructed exhaust.

.
Pull the plug after a few starting attempts and check for gas or no gas. Wet or dry.
If you suspect no gas work backward. A few drops in the cylinder and give it a try. It should start and run a second or two. If that worked clean the carb, check fuel flow to the carb from the tank.
If the blade is not installed the mower may not have enough flywheel effect to start.

I've had a few crankcases with rod punctures that did the same thing, but in the 7 years I've been doing this as a business, almost every problem has been simple stuff.

No one yet with the correct answer. Here is another hint, I can only start the engine with the electric starter once it starts it works as it should. What is the problem

The rewind is assembled backwards and it is rotating in the wrong direction. Don't laugh, I saw this on a Remington chainsaw. Took two of us a couple of weeks to figure it out.

You need to turn the key to the 'ON' position
before trying to start it manually.

I had the same problem with my Ariens SB with 8HP Tec.engine.Would not pull start,but started with electric starter.The rubber primer line was broke,so when I pushed the primer it was not really doing anything.Electric start turned it over faster and it would start.

Cute. What is this? Must be a failed ballast resister....

gorper99 Got the correct answer, I would say 25% of the no starts via pull cord are due to the primer rubber hose rotting off at the carburator nipple.

An engine needs air fuel and a spark we always overlook it is easy to overlook this and we tend to look for more complicated solutions.

What does he win and is it big enough to be taxable? :)

Just a Big Congrats and the pride of been a Winner

Dam and I was going to say that the crank seal was going south , due to a lack of base compression fuel delivery was lacking until elect start increased turnover rate ! Oh well the squirt of gas in the carb or spark plug would have got me to the fuel starvation and priming circuit root cause eventually . Us Canucks might be slow but were diligent ! lol . Your right on the "KISS" rational Rolm .