I am new to all of this, so....

Please help! Just bought a 02 Yamaha Timberwolf 250 2wd. I had to replace the starter. When I started it up the first time there was hesitation when I pushed the start button, about 3 seconds until it turned over. When it finally started the started still stayed engaged. I then put a new solenoid on it and tried again. This time with a new battery, starter and solenoid, when I push the start button the solenoid just clicks. There is plenty of power from the battery and I checked all the connections, even ground. What stumps me is it turned over and the starter engaged the first time, then after I put a new solenoid on it and checked all connections, nothing. I am not sure what that plastic box is with a wire harness going in it, right next to the solenoid and do not know if that has anything to do with my problem. Any advice would be very appreciated. I am ready to get this thing going!