Leaking coolant and car will not start

My car is the LX model. My car overheated about two months back I went to AutoZone and the mechanic checked it out and seen that I had low coolant. So we waited for the car to cool down and we added coolant and then it started properly and the mechanic I went to said it was a thermostat problem and a hose problem. I had those both fixed and the car was okay. About less than a week ago I noticed the AC and the heater were not working properly, the heat would take a long time to start and would be going on and off and the AC was blowing just air. Yesterday I was driving the car and I noticed that it overheated as the needle was at H. I drove a min to my destination and parked the car. I noticed it had no coolant and the radiator was completely drained and then I noticed it was leaking coolant. So I added coolant when the car was cool and tried to start the car but it would not start. The car just clicked. I had my car towed to a mechanic and explained it all to him and he is telling me that he needs to change the starter for $350.00 (parts and labor) first because he needs the car to start to see what the issue is. I am not car savvy but this did not make sense to me so I started to do research and I did not see how it connected. Please anything would be helpful.