I have a 99' Honda fourtrax 300 and I can't get the electric start to work. It's a new battery, new solenoid, and starts with kick start on first try. We have tried jumping it directly off the solenoid itself and can sometimes get a little spark but never starts. Also it's getting power all the way through to the starter itself. Even tried to temporarily bypass (what we believe to be a bad fuse). However there is no neutral light. Would this have something to do with it. Also FYI none of the other handle bar light or brake light work either.
Travis: I just ran into a similar situation so I may be able to help, mine was on a 250 so I assume they are pretty much the same. I would suggest doing the following two things.
1. put a multi meter on the positive post on the starter, and ground out the other end of the mutli meter. It should read some sort of positive voltage when you hit the starter. If there is no voltage you have an electrical problem upstream of the starter.
2. Pull the starter out and bench test it (plenty of youtube vids, I would suggest watching one, and it doesn't have to be a ATV, all starters are the same). Very easy to do, there are two screws (12mm I believe) at the back end of the starter. I access them from the other side where the kick starter is. Once these two bolts are removed you can pull the starter. It takes some force to get it out initially, may need to use a wood block with a light tap of the hammer to get it lose. All that is holding it in is an o-ring and some friction once you remove those two 12mm bolts. Finagle the thing out and put it in your vise. Take some jumper cables and hook up the starter to a battery and it should spin like there's no tomorrow, especially since its under no load. If it doesn't spin your have a dead starter. You can either rebuild it, or buy a new one.
Once you verified these two thing I think we will be able to help you further.