I know you said you replaced the battery, but I would take the cables off and make sure they're clean and tight. If that doesn't fix the problem, trace the red wire from the battery side of the starter solenoid to to the fuse box. Use a 12V test light to check for power going into the fuse. If it has power there, trace the wire coming out of the same fuse to the keyswitch and make sure it has power on it. My guess is the problem is somewhere from the battery to the keyswitch.
Most 4-wheeler problems are caused by a loose nut connecting the handlebars and the seat!!
You only need two tools in life -- WD-40 and duct tape. If it doesn't move and should, use the WD-40. If it shouldn't move and does, use the duct tape.