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