welcome aboard
think about it. it cant be the coil pack or it wouldnt run.....period! since it starts with the rope, it cant possibly be the coil pack, now could it.
since you state it turns over and doesnt fire, it cant possibly be the solenoid either.
I would assume that your starter is not spinning it fast enough or something is wired wrong at the key switch if its not spinning fast, clean your battery cable contacts from the battery to the starter motor and back.