Sounds like your carb was clogged up with oil residue from old fuel left inside it.

A few months ago a friend had the same problem with his engine; no matter what we tried, it would not start. However, when we dropped some fuel into the air filter hole it fired up and ran for a few seconds. It's easy to check btw... just attach some fuel tubing to the carb and blow in it. Some air should be going through the carb and more when you open full throttle. Flushing the carb can be done by blowing fuel through it this way.