Under The Covers: Other Artists Covering Beatles Songs: ‘ All I’ve Got To Do’- Moon Martin. I haven’t heard the name Moon Martin in years. The singer-songwriter, guitarist from Oklahoma got the nickname ‘Moon’ because a number of his songs had the word Moon in them. He had one hit back in 1979 ‘Rolene’ #30. He also was the songwriter who wrote “Bad Case Of Loving You’ which Robert Palmer had a hit with. I see Moon Martin passed away of natural causes last spring at the age of 74. I hadn’t seen that. Martin covered “All I’ve Got To Do’ from With The Beatles on his debut album Shots From A Cold Nightmare.