$68 Homelite gas trimmer at home depot. Ran like crap brand new, adjusted high speed screw out about 1/2 turn, runs like a champ. Actually just got it out today and it started second pull.
Don't pull that carb apart. There is almost nothing in there that moves. Like has been said, the gas is now varnish. The diaphragm pump is most likely cracked. Squirt the heck out of the carb throat with brake cleaner paying attention to squirting some in the little jet. Pull the plug out and do two really quick squirts of brake cleaner in the cylinder. Replace the plug and pull the cord. I promise it will fire on the first pull.