Just to add to the immense wisdom already shared here... learned in small engine class numerous decades ago: The diagnostics for most engines centers around the need for spark, fuel/air, compression, and timing. Start with the easy things and work your way to the more difficult if so inclined.
I have had fuel saturated air filters prevent running. A clogged muffler can prevent running (spark arrester screens carboned up). A loose carb or jug mount allowing extra air into the system is not uncommon on cheap saws. A new spark plug is a no-brainer.
Cedarshark is correct about not using starter fluid. It might damage the cylinder or bearings because of no lube. Just dribble some 2 cycle mix into the spark plug hole.
I learned my chainsaw skills back when Homelite and McCullough were considered top of the line (I'm (getting) old), but falling behind the advancements of Stihl, Jonsered, and Husky.
EDIT: regarding ethanol fuel, I have NOT experienced the problems others mention. I can't figure out why. I DO use stabilized 2 cycle mix,expensive steel gas cans, and rotate fuel at least every 3 months.