The Mississippi-born Dye was bitten with the acting bug after playing the eldest Von Trapp son in a high school production of "The Sound of Music". During his first summer break from college, he went to New York, where he auditioned for and was offered a place in a touring classical theater repertory company. But, as it would conflict with his schooling, Dye declined the offer and returned to Memphis State (now the University of Memphis). A Judd Nelson teen movie, "Making the Grade" (1984), was about to film in the area and Dye won his first professional role playing one of Nelson's prep school buddies. (He would work alongside Nelson again as one of the members of "The Billionaire's Boys Club", a 1987 NBC miniseries.) Dye later won his first screen lead in "Campus Man" (1987), playing an entrepreneurial rogue who pays for his college tuition by getting the hunky guys on campus to pose for a calendar. In 1989, he played a UCLA student living in the school's bell tower in "Big Man on Campus", but after a few more roles, such as "The Best of the Best" (1989) and "Perfect Weapon" (1991), Dye, with the perennial twinkle in his eye, moved into a TV career.

His first regular series work was during the 1989-1990 season of "Tour of Duty" (CBS), when he was cast as a pacifist medic trying to save lives before the battles even begin. Dye played an optimistic medical student juggling the demands of school, working as a bartender and trying to be a single parent in "Jack's Place" (CBS, 1992-93) and was an opportunistic womanizer on the short-lived summer series "Hotel Malibu" (CBS, 1994).