Daneyko was drafted in the 1st round (18th overall) in the 1982 NHL Entry Draft, the first pick of the New Jersey Devils after the franchise relocated from Colorado. He spent several seasons in the minors before getting drafted, and played for the Yorkton Terriers of the Saskatchewan Junior Hockey League, as well as the Great Falls Americans, Spokane Flyers and Seattle Breakers of the Western Hockey League. He then split time between the Devils and the Maine Mariners of the American Hockey League before being called up full-time for the 1985-86 NHL season.