Sounds like the starter relay to me. Try by-passing the relay with a jump lead from the positive terminal on the battery directly to the connection on the starter. If the starter works as it should then I would check the relay and its connections to the start button, the neutral indicator switch and the clutch switch. These are safety interlocks which prevent the starter from working if the bike is in gear and the clutch not pulled in. You can eliminate these by by passing them with a wire direct from the battery to the relay.
Do you have a wiring diagram?
