Two-cycle leaf blower equipment needs maintenance, particularly with regard to dust which can block air flow and foul the equipment. If you follow the recommended maintenance schedule, you are less likely to encounter starting problems. However, if the engine does fail to start, you can follow some troubleshooting steps to fix it.
Check that there's fuel in the tank if the two-cycle leaf blower won't start. Fill it if there isn't any. Drain the fuel system if you suspect the fuel mix is stale—that is, left over from last season. Replace the fuel.
Take a look at the ignition lead and make sure it's not detached from the spark plug. Re-attach it if necessary.
Take a look at the spark plug itself. Pull the ignition lead wire off the spark plug. Hold it by the spark plug cap holder when you pull it. Don't just pull on the wire. Use a socket set to remove the spark plug and look for fouling, cracked porcelain or broken electrodes. Replace the spark plug with a new one.
Un-flood the engine if you suspect it's flooded. Let it drain on its own, or simply remove the spark plug and drain the engine by tilting it.