Here's something I wrote to a customer in 2015 after working with a new carb that I had to install on his Husky 136:
"To start the engine when cold, move ignition switch left and choke it. Do not squeeze the throttle trigger. Pull the cord several times until it pops. Now disengage the choke to automatically set the fast idle. Pull again until it starts. Sounds goofy, but it seems to work. Regardless, you cannot partial choke it together with a fast idle. Once warm, the saw usually starts and runs without a choke and on idle only, but you can set a fast idle by pulling the choke out once and pushing it back in. Squeezing the throttle trigger will always disengage the fast idle."
Not sure if this applies to OP's, but it might. The old carb was a dog and the new one was not that expensive. Suddenly a dead engine roared back to life.