Ariens Briggs & Stratton won't start.

[D_H]

What type of inline tester is this? One with a simple light inside? If so toss it in the trash.

You should test the coil under LOAD. Gap an old plug to 1/4" or 6mm. Ground it out and check for spark.

Some carbs have a pilot jet on top that you can see from the outside of the carb. If yours has this same carb, the pilot jet is plugged with concrete splatter or what ever all that muck is on the outside of the carb.

Bet it needs the valves checked.

Here is the tester I got. https://www.harborfreight.com/in-line-spark-checker-63590.html

I was going to get the Lisle inline tester but it was three times as much locally and twice as much online. I would have had to wait for shipping, so I went down to the local Harbor Freight and picked this one up the other day.

I took the spark plug off again and connected it to the ignition coil. I held onto the spark plug boot while I grounded the end of the spark plug on a screw. I attempted to start the mower and the engine turned over while I did this. I could see spark from the end of the plug over to the nut. Should I have felt anything in my fingers, like a slight shock while I did this? I also saw fuel blowing out of the cylinder through the spark plug hole every time it compressed.

 

[D_H]

Funny.
I have 4 spark testers & the only one I use is a red globe in line tester
If it glows red when attached to the end of a spark plug then there is enough spark to ignite the fuel .
The only thing missing from your list of what you have done is check if the spark is arriving at the correct time
ie:- is the timing key in the flywheel intact ?

The usual method of doing a quick diagnosis is to give the engine a short shot of starter fluid ( I like to use carb cleaner ) down the plug hole.
And with a fresh ( or known to be good ) plug inserted give the engine a couple of good pulls.
If it has resistance to the pulls but does not go bang then either one of the valves is stuck open or the spark is happening at the wrong time .

I took the flywheel off to check the keyway. Two overhead pictures looking straight down onto the top of the flywheel. Pictures attached.

I think everything looks okay to me. I would say the keyway look unharmed.

I also sprayed a little carburetor cleaner into the air inlet and attempted to start the mower, with no change to the mower status.

 

[D_H]

What type of inline tester is this? One with a simple light inside? If so toss it in the trash.

You should test the coil under LOAD. Gap an old plug to 1/4" or 6mm. Ground it out and check for spark.

Some carbs have a pilot jet on top that you can see from the outside of the carb. If yours has this same carb, the pilot jet is plugged with concrete splatter or what ever all that muck is on the outside of the carb.

Bet it needs the valves checked.

Oh, I forgot, I didn't notice any pilot jet on the top of the carburetor.

 

[slomo]

Here is the tester I got. https://www.harborfreight.com/in-line-spark-checker-63590.html

I was going to get the Lisle inline tester but it was three times as much locally and twice as much online. I would have had to wait for shipping, so I went down to the local Harbor Freight and picked this one up the other day.

I took the spark plug off again and connected it to the ignition coil. I held onto the spark plug boot while I grounded the end of the spark plug on a screw. I attempted to start the mower and the engine turned over while I did this. I could see spark from the end of the plug over to the nut. Should I have felt anything in my fingers, like a slight shock while I did this? I also saw fuel blowing out of the cylinder through the spark plug hole every time it compressed.

That tester verifies you have spark (no load). But not enough to fire the plug while running (under load).

That test sounds like the spark is leaking out of the insulation. Hook it up and don't touch it. Again the tester you have is not conclusive enough for an engine to run proper. If you have a weak coil, might not be strong enough to fire across the plug gap under compression.

How much fuel was blowing out? Like wow or a small trickle? An excessive amount would be the carb needle and seat hanging open.

 

[D_H]

In addition to what I've already said:

I feel I should inform that I changed the oil and filter at the beginning of this season, probably around February. The oil I put in at February this year was 5w30 synthetic. The manual says that is okay to use. When I changed it again this year last week, I noticed the oil was pretty black and the spark plug had a little bit of buildup on it. Again, right now the oil and spark plug are brand new. I've taken the spark plug out a few times (testing) and it does not have any grime or build up on it now.​

 

[slomo]

I use a timing light for spark detection

Visibly that will check for spark. But is it enough to fire across the gap under compression? No way of telling with a timing light.

Either gap a plug to 1/4" or 6mm or get a real tester like the one below.

 

[slomo]

In addition to what I've already said:

I feel I should inform that I changed the oil and filter at the beginning of this season, probably around February. The oil I put in at February this year was 5w30 synthetic. The manual says that is okay to use. When I changed it again this year last week, I noticed the oil was pretty black and the spark plug had a little bit of buildup on it. Again, right now the oil and spark plug are brand new. I've taken the spark plug out a few times (testing) and it does not have any grime or build up on it now.​

I would stick with the ol' tried and true SAE30 oil. Briggs says 5w-30 will consume more oil and to check the level more often. Don't have to do that with SAE30 oil.

 

[slomo]

Check the oil dipstick and smell for fuel.

 

[slomo]

I took the flywheel off to check the keyway. Two overhead pictures looking straight down onto the top of the flywheel. Pictures attached.

I think everything looks okay to me. I would say the keyway look unharmed.

I also sprayed a little carburetor cleaner into the air inlet and attempted to start the mower, with no change to the mower status.

Key looks okay to me.

 

[D_H]

How much fuel was blowing out? Like wow or a small trickle? An excessive amount would be the carb needle and seat hanging open.

It definitely was not 'like wow' I would say. Seemed more like a small trickle I guess. Several drops/small spray amongst a mist of fuel every time the engine had a revolution.