I have a 2 year old Tecumseh yard machine snow blower. It started up fine the first year. This year, it wouldn't start. I've only used it 4 times since I've had it. Does anyone have an idea on what this could be? I'm thinking I might have left some gasoline in it the last time I used it.

Gas can "Varnish" or go bad. You will probably need to drain gas, clean tank, some carbs have a float bowl drain plug. May get lucky witrh carb cleaner sprayed in drain to loosen,
When good fuel is able to be provided, may help to prime, teaspoon of good gas in plug hole, or blast of starting fluid. Not too much, Engine needs lubrication. This will determine you have spark, you probably have compression, last needed item is Fuel.