In these cases the main thing we have to do, is get the symptoms clear. From what has been posted, the engine started once when primed with petrol, but did not start when the experiment was repeated. It could, as you said, have been rich the second time, but if you pulled the starter two or three times, it should have cleared that and started. Hence deviosi's concern that your problem might be weak ignition.
It is easy to test the ignition system. Just set the controls in the start position. Remove the spark plug from the cylinder head. Reconnect the lead to the spark plug. Clamp the metal body of the plug to the cylinder head. Pull the starter cord while watching the gap between the two electrodes on the end of the plug that is normally inside the cylinder head. You should see a rapid, even series of blue flashes across the gap. If the flashes are red, or uneven/intermittent, or if you only sometimes get flashes at all, some part of your ignition system has failed and that is probably your only problem. In that situation the first thing to try (after making sure you did the test correctly) is a new spark plug. If that doesn't cure the problem, come back and tell us, and we'll take it from there.
