So here is the first aired show. As I stated in Saturdays post the Song and characters are different. Now to the answer to the question, it is the Radio. In the un-aired pilot (posted on Saturday) the radio was swallowed by a fish. In this, the first aired one, the radio appears only one time and not again. As to the song the one that appears in this video is the one we are all familiar with. The characters are very familiar, since these are the ones we are use to seeing on the TV series.
Gilligan Island ran for Three season, from 1964-1967, The theme song was different in season one than in seasons 2 and 3. Interesting note, the Professor and Maryann were referred to as "and the rest" in the first season. Then in the second and third season they got billing and their characters name were placed in the title song. That is the one most people remember.
This is the first aired Show. Listen closely to the tile song. Next Saturday I will post one from the second season.
Video courtesy of WB