Wow, I noticed a yellow spark when I was testing the plug and didn't even know that was a thing. That is awesome. I'll be ordering a new coil today
As someone else said earlier, do a thorough and proper diagnosis before you throw more parts at the machine.
This happens way too often with homeowners and by the second or third attempt they stumble into it and get it right and it just creates positive reinforcement of doing a bad pattern in the future.
I understand it's frustrating you have to do something but we need to back up before you waste money on a coil and like someone else said make sure you order one off eBay or Amazon so it will be $16 shipped to your door instead of paying 60 at a lawnmower shop or for a Briggs & Stratton brand.
Two of the carbs flooded out one wouldn't run it all but the question now is if you take the plug out and put a fresh dry plug in there can you get it to run on carb cleaner spraying it in the intake of the carb????
If you can then it certainly isn't the coil at least not unless it runs for a while and gets hot and then they coil breaks down and then it dies and then starts the process all over again once it cools off but that's a secondary diagnosis. You are well before that now.
Also, make sure the spark plug is gapped no greater than .030.
That is the spec but I like to get them about .027 to .028. in fact, it makes little difference as you could gap it at .020 or .025 and you wouldn't notice a bit of difference in the performance or the power but as it gets older and more carbon on it and the coil gets weaker or if the coil is getting borderline and ready to fail in the next couple of years anyways, it will last longer and you'll get a more consistent stronger spark with a smaller gap.
So tighteris better than looser on the spark plug gap -- within reason!
So get back to the basics. If the cylinder isn't flooded out and the plugs not wet now you just want to make sure the plug Sparks when you spend the engine over by looking at the spark jumping at the tip and it should be a bluish to whitish color. Red will still fire and run but it is weaker and yellow you really hardly ever see I guess unless it's bright and sunny out and it's hard to see anything.
If the cylinder is dry and the plug is not fouled out and you spin the engine over at normal speed and provide a fuel source into the intake, if the engine is mechanically sound which means the valves working properly and having compression and having spark...it will run for a few seconds until the fuel source you provide runs out.
In fact, you could take the carburetor off and lay it on the ground and squirt the carb cleaner in the side of the engine where the hole is and it would do the same thing but that's not a good idea because they will be no method to govern it and you could overrev and blow it up or grenade your internal governor/slinger because with no carb on the engine to block off the air flow the only way you have to stall it out until it runs out of fuel is to put a thick rag over the hole and kill its intake of air which is a little hard to do.
My point is that the carb has nothing to do with the engine actually running or not.... Providing fuel and at the proper amount and ratio is what determines whether it a mechanically sound engine will run or not. That just happens to be what the carburetor is supposed to do.
So go get that can of car cleaner or a little spray bottle and pour some gas in it and check your spark plug and see if this thing will run for three or four seconds at a time on an external fuel source.