The correct answer is option 4, James A. Hickey. He is credited with starting the first newspaper in India. It is important to note that the newspaper referred to here is "The Bengal Gazette," also known as "Hickey`s Bengal Gazette." This newspaper was published in Kolkata (then Calcutta) in 1780. While the other options listed in the question are important figures in Indian history, they were not directly involved in starting the first newspaper in India. Dadabhai Naoroji was a prominent Indian political leader, W.C. Bonnerjee was a lawyer and a founder of the Indian National Congress, and Rabindranath Tagore was a poet, philosopher, and the first non-European Nobel laureate. Hence, James A. Hickey is the correct answer for the given question.