Considering the mileage and it 'sat' for years I would suspect insuffient fuel delivery. Disregard airfilter or muffler, compression/vacuum problems unless the previous owner failed on maintenance. Combustion is designed as 50 parts air to 1 part combustion fume the air part not so critical.
Remove and replace the fuel line but don't hook up to the carb yet drain the tank dry, the tank may have or probally does have crude on the bottom you want to wash that out first. Than refill w/ 2C oil and 92 octain mix because this is a HC engine.
Another issue is the Puch poorly made HV cable, the metal cap one get rid off it and replace it w/ any solid US made modern lawn mower cable.