Try jumping the wires for your starter at the starter solenoid, it should be under the seat (mine is for an LTA-400F). It will look something similar to this
Use a screw driver and touch the two posts with the two large wires.
If it starts then it is either a wiring, solenoid, or switch issue.
If it does not start then check the voltages on the large posts one should be 12+ volts the other should be 0 volts. If both are 0 then you have an issue with the cable coming from the battery. Now while testing the one with 0 volts push the start button it should jump to 12. If it does not then continue on to my next paragraph. If it does then continue on down the wire and check the voltage at the starter motor and see if it is reading 12 volts. If it does then check the grounding for the starter make sure it is good. If it does not then there is possibly a break in that wire. You can also directly test the starter by using jumper cables put the negative on the Atv frame and the positive on the starter positive and it should turn over. If not then you most likely have a bad starter.
Now if you are not getting 12 volts on the other wire or it does start when you jump the wires.
Check the other set of wires going to the solenoid see if the voltages change when you push the start button. If they do then you have a bad solenoid if not then it is probably a fuse or start switch or broken wire somewhere along route from the switch to the solenoid.
Let me know what you get and I will try to help you further