Complex sentence: Brian, worried about the group's future, asked his father to help them make more recordings but Murry and Hite Morgan, who now was their music publisher, were turned down by a number of Los Angeles record companies.
Split into simpler sentences: Brian, worried about the group's future, asked his father to help them make more recordings. But Murry and Hite Morgan (who at this point was their music publisher) were turned down by a number of Los Angeles record companies.