I am new to the atv repair world, but have some similar experience with start problems on an old boat I used to have.

I picked up the atv from my father in law a couple of weeks ago, he said that it has electrical problems. I bought a new battery and did some initial test, Headlights good, tail lights good, no start, replaced the fuse at the starter relay. I tried to jump the two posts on the relay and did this three times and it started to turnover, starter sounded good no gas. I came back to try this again and nothing, What could be the problem? I did try again this morning and tried for a split second. I have ordered the repair manual, but have not received it yet. Just wanted to see if anyone knows how to move forward. Thanks

 

Check the ground wire connection to the engine. Paint/rust may be preventing a good contact between the connector and the engine case. If engine starts fine with the pull-start, that's it.

 

Do you know if the quad had a funny smell when it was running? Our one did then the problems started. We ended up replacing the voltage regulator and the C.D.I box with after market parts. Oem is real costly, all the electrical problems are gone. We had lights fail and it would turn over, but not start . It was making a strange smell before all this for a few weeks. I hope this helps!

 

I should have been more specific.
Follow the ground (negative) wire from the starter relay. It would be routed toward the left side of the engine. See where the wire end is attached to. Remove the screw/bolt and check the connection as I described above.