My first guess is a stuck butterfly valve or needle valve in the carburetor throat due to "varnish" accumulated over the winter months from evaporating gasiline (your petrol). When you press the accelerator trigger, you're actually opening the butterfly valve to let in more air and the needle valve is where that air/fuel mixture enters the combustion chamber.
Here's a good pictorial link:
http://www.ankn.uaf.e...s/vs/carburetors.html
Additionally, always check the condition of the air filter, since on chainsaws it can easily clog.
Lastly, next winter be sure to drain all the fuel (including from the carburetor and bowl) or run it for several minutes after adding a goodly amount of Sta-bil or other recommended fuel additive for over-winter storage.