the problem lies somewhere either in the push to start button..or from his starter relay selonoid to the switch
If this is the case, then it would start when he crosses over the solenoid, but the said it quit starting like that.
and if i were him..i would jump the starter relay with a screw driver at the connections on the relay
I believe, in the first post, he already said he had been starting it this way and it quit starting that way. Then, he said he had to start pulling the rope while he was crossing the solenoid. To me that sounds like he was just turning the engine over and helping the starter. Maybe the starter was weak. Then, he said it quit starting like that and will only start by pulling the rope now.
I don't understand this, though, because if the battery is good and the starter is good and he is crossing over the solenoid, it would have to crank over unless he has a bad battery cable or starter cable. When you cross over the solenoid, that is bypassing the solenoid and running the power straight from the battery to the starter. I would check the cables and I would check all the grounds on the ATV.