Why won't my lawnmower start?

It's a push mower, you have to pull the cord to start it. It has gas, the spark plug is clean and plugged in, the bottom (underside) is clean and it isn't flooded (pushed the primer button 3 times as directed but that's all). It ALMOST turns over but doesn't hang on ... and it's only 2 years old. What can I do to make it start? Thanks so much!