Car wont start after icing snow

It was snow all over my car night. This afternoon, the ice melt. But my car wont start. The battery completely dies. So I use a charge cable. Then battery back on and the instrument lights on also. But it just cant start. I heard very slow crank sound, but just cant start. As I remove the charge cable, the battery immediately completely die. The battery is 1 year old. Need help. Thanks.

PS: I got a scoop on my hood. Is that the problem that lead the melting water goes in?