It's been a while since I've handled a pull start, but since it's something most people will be familiar with, I'd have a little fun with it (provided the tone of the story allows for that). He jerked the starter chord and the motor snarled at him like a lazy dog warning him to leave it alone. He tried again, but still the motor wouldn't spark.
The motor coughed and sputtered, declaring its protest with a cloud of blue smoke and a silent refusal to start.
Funnily enough, I've had a discussion in the middle of the mountain road last month with a dude that was repairing the asphalt holes on his own because the town hall wouldn't do it. In the middle of the thing the motor had stopped working so he was trying to start the motor on what is effectively a handheld asphalt press. He was very kind to this lost tourist for someone stuck in the middle of nowhere with a at least 200kg of dead machinery. While giving me much needed directions to wherever I was supposed to drop my tent, he kept trying to start the motor to absolutely no effect. The chord zipped, the beat of the piston rose, he was hopeful but no luck. Every time the beat died down pathetically and he looked at me sadly as he went on a tangent about the young people leaving this country for work and buses that only come once a week. I left them there after a while to get to my campsite before they closed admissions. The old man, his pick up truck, his machine that went Tuh-tuh-tuh on the road riddled with half filled potholes. OK I might have had too much fun with that one The scene is real btw. It was a very weird but enjoyable interaction.
"The whine of the rope as it unreeled from the pulley rose in pitch, morbidly coordinated with the sputtering of the single piston rattling in its cylinder and the slap of the valves slamming shut deep in the heart of the lifeless engine."
Like a man suddenly awoken from a deathlike stupor, the motor gasped a raspy, sputtering breath. The hope in your heart flickers when you hear it, until you realize it was no living breath, but the breath of a dead man after all.
This. Keep it simple. Your reader only needs to know it failed to start. They’re honestly not interested in reading a lengthy paragraph describing the sound. Well, this reader wouldn’t be, put it that way.
I pulled the cord, and pulled again. Pulled till my shoulder ached. The motor, it chuffed, it burbled, it gurgled..it refused to fire up. My beloved lawnmower had lost its purr.
Try some variant of popple. "When he yanked to rope, the engine poppled a couple of seconds and fell silent." Cough and pop are also onomatopoetic.
