Well I messed with the carb a tad bit and pulled it started for about 5 seconds..... then it'll still do that just wont stay running
some times when a carb sits for a while the idle circuits will get crud in them from the gas sitting and breaking down,,, especially if it is ethanol blended fuel,,, Try backing the L&H needles all the way out Pay attention to which one goes where,,,, the L is usually physically longer than the H if so,,, pretty easy to keep them going back in the right holes,,,
get a can of spray carb cleaner with the nozzle on it (put some safety glasses on,,, gotta have PPE!!!) hold the carb out away from you and manipulate the carb and throttle plates open where you can see into the venturi,, place the bussiness end of the nozzle in each adjustment hole and spray them good the L circuit wont flow as much volume as the H will but you should have full streams,,, if the L looks weak and more cleaner is blowing back out around the nozzle then the ildle circuit my be plugged a bit,,
be careful not to get the cleaner in you eyes,,, don't ask me how I know,,, if its plugged bad enough I have removed the covers and rodded out the circuits with a very fine wire,,,
an utlra sonic cleaner is the best method,,, but I dont know how you guys are set up....
let is know what you find out,,, also if the saw has one,, make sure the intake boot and impulse hose is intact
keep diggin,,, you'll get it,,,