3 things are needed. Spark, fuel, compression (assuming the timing is correct, which it should be)
You need to find out which one is missing, but it seems like you already have.....fuel.
You don't simply have a fuel shutoff valve that's still shut off, do you?
If, after trying to start the snowblower (turning on the choke to full on/closed, throttle to full on, pumping the primer until gas comes out the carburetor) and it still doesn't start - take out the spark plug to see if it's wet. If not, there's a fuel problem. If it's dry, spray some starting fluid or pour some gas in the hole before putting the spark plug back in tight. See if it will start and run for a second or two. If it does, you've determined that there's a fuel problem. As previously mentioned by others, buying a new carburetor is the easy fix for this. They are pretty cheap also.
If it still won't fire after giving it some fuel directly, you have other problems.
If the spark plug is wet, but it didn't start, check the spark plug for spark. Remove it, lay it on its side on the engine (still connected to the spark plug wire) and check if there's a spark at the tip. You need to make sure it has good contact with the side/threads of the spark plug and the engine. If no spark, try a new spark plug. It can be most any spark plug you have lying around. If still no spark, you have a problem with the ignition system. Snowblowers often have a key (might be just a plastic key) that when pulled, grounds out the ignition system so it won't run. This is an area I'd check to see if something came disconnected or rusted off or bent or otherwise messed up.
When pulling the rope to start the engine (with the spark plug in and tight), there should be resistance when you pull it over. If there's little to none, you have a compression problem.
