Assuming it's a 2-stroke, they are very simple engines in design. Besides checking for spark and it's getting gas, check for an air leak. This could be the carburetor gasket AND/OR the seals on the crankshaft. Worked on a Tanaka aircooled outboard that refused to start, the problem being the upper seal on the crankshaft was completely out of the block. Another item to check is the reed valve.
Looks like a four stroke, Tecumseh based engine, from the model number drawing. Remove the air filter and try to start it normally. They can sometimes plug up solid. If it won't start then, figure out a way to put a small amount of gas into the throat of the carb (where the air filter goes) and try pulling that over a few more times. If it starts, run and quits, that means spark and compression are acceptable and you have a fuel delivery problem, most likely being a dirty carb or water in the fuel, from the stupid ethanol gas.
I have also seen one case where the blade brake ignition cut off, under the flywheel, was partially shorted out, causing your same problem. I'm not a professional mower guy, though; so I don't know how wide spead a problem that is. I know fuel problems are by FAR, the most common.
