Is the number stamped on the metal part I posted earlier the right number?The engine numbers are stamped in the top of the valve cover. Looking at the pic of the starter side of the engine, the starter gear looks to be meshed with the flywheel gear. That should not be the case. The starter gear should be in a lowered position and will jump up when the starter turns. If you turn the top of the engine, the starter gear should not move. You can free it up with some WD-40 or other light weight oil. Turning the gear CW should cause it to travel down it's shaft. CCW, it should come up. You can loosen the starter mounting bolts the get more room.
Once this is correct, remove the spark plug and the engine should turn easily by hand. If not, something is locked. If free, then try and start with the key. It won't cuz the plug is out, but it should spin. If it does spin, put the plug back in and see what happens. If it only starts with spray in car, you have a fuel problem. Carb or supply. If it's locked, I would remove the valve cover and see if everything is intact. A push rod may be bent, or missing or the rocker arm may be loose. There are many videos on how to repair\adjust the valve train.
If everything looks proper and you have fuel to the carb, I would order a HIPA brand carb from Amazon and install it. It may solve all starting issues. Stay away from other cheap carbs. Let us know your results.
It appears that the Fuel Filter is installed backwards. Big end to the Fuel pump is the norm. It makes a difference on some systems. Remove Battery connections both ends, clean and recharge battery.My husband said what he can see of the fuel seems to run properly but engine will not crank. We were unable to work on it for a couple weeks after catching the rope and after removing the rope and making sure the blades spin freely, when he first started it is when it has backfiring and and a tiny bit of black smoke, It was at that point he decided to try changing the fuel filter in case that was the problem and that's when it got worse. The one we thought was correct had same a shape as the one on it but the inside was different. He changed back to the original fuel filter after seeing it looked ok but now won't start or even crank. I have a couple short videos I took this morning of the latest sounds but it won't let me upload them here. I am uploading a couple of pictures in case they may help.
Help on this forum is greatly appreciated. I don't want to end up paying someone to come get it and work on it just to the me its a loss, especially after we put new more aggressive tires on it shortly after getting it to help with traction when pulling the garden cart up hills to shed and gardens.
Don't start what they can't finish.....Any chance you might have sheared a key and the engine is out of time?
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Stop it. Just making it worse.You have to pull the flywheel. If you post the mower model#, someone may be able to point you to documentation. There's usually a plate or sticker with model and serial numbers. It's usually different from the model it's sold as. There's usually a cover on top that has to come off, then you can get to the flywheel. A normal socket set should work, though you have to stop the blade while you turn the nut. Here's a starter, but probably doesn't cover this. https://www.manualslib.com/products/Craftsman-Yts3000-6027247.html