I have a Husqvarna 345, I always used non-ethanol fuel. Like 10 years ago, the throttle lock on top of the handle broke, so I removed it and duct taped the spring in the down position and used it like that every since. It has always started right up every time, even after no use in months. I pull the choke, push in the pressure release pin, pull the rope three times and the engine turns on and then quickly off. I push in the choke, crank it once or twice and it turns on perfect. The last few times I used it, I started to notice that the saw will turn off if I let it idle for a minute or so, and it kept getting worse, it would turn off quicker. My solution was to just hold it in my hand and keep the trigger down a tad to make it idle faster to keep it from shutting off. I noticed now that it will start every time if I pull the choke out then push it back in before I pull the starter rope and it will idle faster and the chain will turn, but as soon as I squeeze the trigger, the engine will shut off. I looked at the air filter and it is spotless, I looked down the barrel and it is spotless. I played with the L, T, H adjustment screws and it made no difference. As soon as I squeeze the trigger, it shuts off. So, I looked at how the carb choke and throttle levers work ( see pictures) and noticed that when you pull the choke, not only does it close the choke butterfly but it also pushes the carb throttle lever a tad faster. When I push the choke back in, the choke butterfly opens, however, the choke lever that accelerates the throttle, does not disengage, it remains accelerating a tad the throttle lever on the carb. This I assume is normal operation and it is why the engine revs at a higher idle speed before and the chain turned, till I pushed the trigger. The trigger disengages the choke lever to the throttle, then the engine is at true idle, not fast idle. Now when I press the trigger, the engine goes to normal idle and immediately shuts off and unless you pull and push in the choke, therefore setting it in fast idle, the engine will not turn on. How can I fix this problem?