Do not make this harder than it is.
If you checked for spark and it had it, but would not spark through the spark plug, try another spark plug.
They do go bad. Also make sure the plug is gapped correctly.
Did you leave any gas in it over the winter?
Old old was the gas you put in to try to start it?
If you are holding the plug wire, it should shock you enough to force you to let go, or at least make you cuss and wish you had.
In order to test the spark using the spark plug, you must ground the plug against a head bolt to get good ground.
Then you should see spark..
Gap plug at 30/1000 of an inch.
You can not leave gas in over the winter at all.
I will get to that in a second.
Will it start and run even for 10 seconds if you pour a teaspoon of fresh gas in the intake after removing the air cleaner?
If so, then the carburetor is dirty.
As engines sit or get older, fuel that is left in the carburetor can turn to gum and varnish and cause this and other problems. Also, any gasoline that was left in a gas can for a period of more than 30 days must be discarded because it also has begun to turn to varnish.
Today's gasoline's contain MTBE and alcohol. (Ethanol) They turn to "Junk and garbage" very quickly. Alcohol is partially water (H2O). And they call it "Oxygenated fuels! It is the oxygen that breaks down the organic compounds in the fuel and turns the gas to "Garbage" (Gum and varnish) The fuels we had just a few years ago had no alcohol in it and would store for longer periods of time before going stale... and fuel stabilizers do almost nothing to prevent the fuel from going bad with the changes in today's fuels.
Do not buy gas from the "Discount" Stations. The discount stations get a reduced price on gas because they may be buying fuel that is nearly 30 days old already. You may be getting fuel that's nearly stale right from the pump when buying from a discount station. Purchase your fuel from the well-known stations such as Shell, BP, Sonoco, Phillips 66 etc.
More than 70% of all of our repairs in our lawn mower business are due to this same issue. You most likely have dirt, gum, varnish...etc in your carburetor plugging up the small passageways and jets in the carburetor.
The carburetor must be removed from the engine. Clean all parts with carburetor cleaner and blow out all the small holes and passageways with compressed air. Remove all of the non-metallic parts since the carburetor cleaner will cause them to be disfigured decompose and plug the carburetor as time goes on.
Wash the carburetor cleaner off of the metal parts by washing them in warm, soapy water then rinsing with clean water. Dry them by blowing it off with compressed air. Make sure that all the passageways are blown dry before reassembling.
Reassemble using a NEW carburetor rebuild kit.
DO NOT TRY TO REASSEMBLE WITHOUT USING A COMPLTE CARBURETOR KIT! You will just end up having to do the job again.
ALWAYS clean the fuel tank and replace the fuel line when doing this repair or you may have to do it all over again. The inside of the fuel line disintegrates over time and these small pieces of rubber will plug up the carburetor too. Dirt and water from a dirty fuel tank will also plug up the carburetor. Find the Model, type and serial or code numbers off of the engine and take them to your local dealer to get the carburetor repair kit.
If you do the work yourself, take pictures or at least make a drawing of where all the linkages, gaskets, and component parts go. Correct reassembly is critical.
If the carburetor still doesn't work correctly, you may have to take it to someone who has an "Ultra-sonic" cleaning machine. This machine uses carb cleaner and ultrasonic vibrations to get the very small passageways clean when traditional methods fail.
If you don't feel comfortable with this kind of repair I would suggest sending it to a reputable shop.
Feel free to contact me here at this question anytime ...even after you hit the "ACCEPT" button ...and I will try to help further.
Let me know also about the spark issue.
Make sure you get all the old gas off the spark plug.
The gas you put in the tank is probably now junk.