My Homelite chainsaw wouldn't start. At all, nada, wouldn't even sputter. The gas in it was very old, and it hadn't been started in over a year. I emptied all the gas out of it, pulled the spark plug, and took off the air filter (cleaned the filter and plug). I pumped the primer enough times to empty it. Then made sure the thing was completely empty of old fuel. I then shot a bunch of carb cleaner down it's throat, and poured about a cup of a mix of paint thinner, carb cleaner, Techron and brake cleaner in the gas tank. I then pumped the primer a bunch of times to pump that "cleaner mix" into it, set the chole to full on and opened the throttle all the way. I pulled the starter cord a bunch of times, primed more, pulled more, primed more, pulled more, etc... until I saw a mist of stuff blowing out the spark plug hole when I pulled the starter rope. I did this a bunch of times, like a hundred or so, then sprayed more carb cleaner down it's throat. Unorthodox I know, but it did clean the carb and get the crap and varnish out.
After that, it seemed to me that I had successfully cleaned the crap out of the fuel system, so I emptied the rest of that cleaner mix out of the tank and pumped the primer to empty it as well.
I then squirted a little engine oil in the plug hole, turned the engine over a few times and put the plug back in. I then refilled it with fresh gas/oil mix, and added a little Techron to the gas.
I pulled the rope a few times, it sputtered, and after a couple more pulls it started right up. Initially there was a big cloud of blue smoke that went away after about 10 seconds of running. Now it's running just fine again.
You gotta keep fresh, clean fuel in them and don't let them sit unused for a long time with gas in the tank. If you're going to store it, empty the tank and start it and let it run dry. If I let my mower sit all winter with fuel in it, next time I try to start it, it takes a bunch of pulls then it runs like crap until I get fresh gas in it.
You'll have to do whatever is needed to clean your carb out.