From what you say, it sounds to me as if this a fuel problem. (I stand to be corrected!)... if it starts and runs for a short time I recon the ignition side must be Ok.
Make sure the fuel is new (a long winter stay in the shed can have the fuel going off) try and remove any covers to expose the carb' you may be able to fiddle off the float bowl, if it has one, for cleaning. Some may have a fuel tap on/off that may have a filter to clean. Check also for split or damaged fuel pipes. If the spark plug has never been changed, do this, as it will help too.
Terry.
April 2006