In October 1976, Parker made his Broadway debut as an understudy at the
Morosco Theatre in a revival of the play
The Innocents, adapted and directed by
Harold Pinter. He and his siblings performed in a touring production of "The Sound of Music." He played Doctor Dillamond in early drafted scenes that were cut from the final version of the musical. After over two years in the Broadway company, making him the longest-running Broadway Dillamond to date, he played his final performance October 31, 2010. After a year away from the show and Doctor Dillamond, Parker returned to the role in the Second National US Tour company, marking his fourth North American production. He replaced
Martin Moran on December 20, 2011, and he played his last show on September 30, 2012. From March 20 through April 14, 2013, he returned to the first touring production, where he created the role in 2005, covering in the absence of
Clifton Davis. On September 23, 2014, he returned to the show on Broadway, replacing
K. Todd Freeman as Doctor Dillamond and played his final performance on January 31, 2016. ==Naked Angels==