My '03 Kodiak starts in Park or Neutral, but the gear indicator light has to be on. Sometimes I need to shake the rig a bit to get the light on. I agree with the others - you may have a switch or wire that's gone bad.
Same here, for my '03, neutral or park, light must be on.
Alternatively, if I pressed the rear brake pedal (or squeezed the handle), I could start it in gear. Had to tear the front end apart to replace the coil pack, and got something out of adjustment when putting it back together, because now I can't do the brake pedal starting, it must be in neutral or park now.