give your saw a good cleaning ...
Opening the fuel tank to refill the tank causes a change in behavior. It releases any vapor pressure in the tank and fuel line up to the carb, which vapor pressure was sufficient, e.g. saw functioning perfectly, when the "closed" tank of old gas was approaching empty. Opening the tank changed the "balance" between the vapor pressure in the fuel tank and the greater vapor pressure in chassis of the cooking carb. The old fuel, under the liquid side of the fuel pump diaphram, is now "hoter" than the new fuel in the tank, and the vapor pressure (proportional to liquid temperature) in the well of the fuel pump, and on both sides of the metering needle, is so much greater than the "supply" pressure in the fuel tank, that the positive and negative pressures on the operating side of the fuel pump diaphram are not sufficient to overcome the difference, and get things going. vapor lock.
If you don't have a thingie button on the bottom of your carb to release pressure on the regulated side of the metering chamber and on the high side of the metering needle, in the fuel pump well then you have to find another way to release the vapor lock ... maybe try kneeling down on your right knee behind the saw, which should be on level ground with the bar free, and chain unable to grab any nearby objects, ground, etc. With your right hand and arm, hold the rear handle "a little high," e.g. toward the body of the saw (so as to gain whatever mechanical leverage over the entire saw you can) and put the sufficient weight of your torso down on the saw, so as to press the *entire flat bottom of the saw safely *down against the ground, and so as to keep the bar up and the saw steady when it starts. If you want, put a 2' stick into the handle bar and hold it down with the left foot. Pop the starter chord with short strokes with the left hand, angling the pulls a little backward (e.g. along the restraining force of the right arm, and not straight upward as usual), while holding the throttle wide open ....
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I forgot the most important thing ... what caused the carb to lose its normal cooling capacity? Clean your saw ... I'm going to guess ... the film (or cake) of oil impregnated sawdust that has probably accumulated on the sides of your carb act as a heat insulator, so that it is not getting the cooling it should from the intake air. That also probably means the ignition system is similarly coated (due to internal resistance, hot ignition systems produce cold sparts). If the carb box is caked up, the cylinder fins are probably coated up too. Why the sawdust-? Maybe the saw is trying to tell you that it don't like dull chains.