Start problem

Yesterday I changed the headlight bulb of my G20. Following the manual, I tried to disconnect the negative cable of battery, but beacuse of the corrosion, I could not disconnect it. The negative side of battery is a little bit loose than before. After I got bulb changed, my G20 cannot start. I think the battery works since all the lights and radio work fine. Before I change the bulb, the car start well.

I am wondering whether the start problem is because I made the negative cable of battery a little loose. Or it is a real starter problem. Thanks for any suggestions.

I forgot to mension that it is a 94.5 G20. The starter was changed about 2.5 years ago.