Check if the saw will start/cough if you spray ether/quick start into the air filter. This will rule out any valve problems.
Make sure you are using the correct fuel/oil mixture. Had a friend who’s dad bought this “special” oil that mixed 20:1 for every 2 stroke known to man. He spent days trying to fix his weed eater until I looked in the manual and found out that it needed a 40:1 mix, mixed up a batch with regular 2stroke oil and gas and bang, it ran fine (OK, I needed to re-tune it since he fiddled with the needles). If you don’t know the right mixture, mix Stihl or Husqvarna 2 stroke chainsaw oil at 40:1 and use this to test. It may be a little lean, but if it starts, this could be the problem.
If it coughs/runs with the ether but not with the new gas, remove the carb and try blowing through where the gas line is attached. If you can blow through it, gas should be able to go through it also. If not, there is a blockage somewhere in the system.
First try the mixture screw. Seat it mixture screw all the way in (turn lightly until it won’t turn anymore, BE GENTLE), then open it up 1 turn. (The owner’s manual may have this information). Also, like mg.greg said, if someone mashed your jets, you’re out of luck.
Most chainsaws have carbs that are designed to be used in all positions, so they don’t have float valves, just membranes to keep the fuel from leaking out. If the membranes are filled with dirt, they won’t let the fuel through.
If you still can’t get air through, try to follow the fuel’s path, and blow though each hole with compressed air. You should be able to find the obstruction that way.
Also blow through the supply hose from the tank to make sure it isn’t plugged.
If fuel is getting through, try to start it again and see if you fixed it. If not, chech the spark plug. If its wet, fuel is getting into the saw, but not burning. Could be too rich (try screwing the mixture needle in) . Try taking the choke off.