There are two possibilities now that could cause this problem.
First make sure you are using PREMIUM gas. Regular 87 octane fuel will ruin the engine on a two-cycle. You get what is known as detonation and it will score the piston and cylinder. This is especially true in the last 4 or 5 years since they changed the formula of gasoline and turned it to garbage.
Now as to your problems....
You either have low compression in the engine caused by a scored piston or cylinder.
This could have been caused by the poor gasoline as outlined above or could have been
caused by poor quality oil of lack of oil at some time in the saws life.
The other possibility is that even though the carburetor seems to be in good shape, it probably is not. Even if it only had 5 hours of use on it.....you probably need to COMPLETELY rebuild the carb. The diaphragms probably are a little bit stiff from sitting.
Please see my stock answer below for more information on this. I hope this helps.
As engines sit, fuel that is left in the carburetor can turn to gum and varnish and cause this and other problems.
Also, any gasoline that was left in a gas can for a period of more than 30 days must be discarded because it also has begun to turn to varnish.
More than 70% of all of our repairs in our lawn mower business are due to this same issue. You most likely have dirt, gum, varnish...etc in your carburetor plugging up the small passageways and jets in the carb. It Must be removed from the engine, cleaned very well, blown out with compressed air and reassembled using a NEW carburetor rebuild kit. ALWAYS clean the fuel tank and replace the fuel line when doing this repair or you may have to do it all over again. The inside of the fuel line disintegrates over time and these small pieces of rubber will plug up the carb too. Dirt and water from a dirty fuel tank will also plug up the carb. Find the Model, type and serial or code numbers off of the engine and take them to your local dealer to get the carb kit.