A familiar face on the small screen as well, Parker made his TV debut in "Don't Touch", a 1985 "ABC Afterschool Special". This was followed by a part in the 1986 CBS docudrama "Courage" starring Sophia Loren as a mother who joins the war on drugs and becomes a decorated DEA agent after finding that her son (played by Parker) was an addict. The next year, he appeared in another CBS docudrama, the miniseries "At Mother's Request". From 1989 to 1990 Parker was featured in the recurring role of Lee Owens, the young housepainter boyfriend of Melanie Mayron's Melissa Steadman, in the ABC drama "thirtysomething". He moved on to series regular on the short-lived legal drama "Eddie Dodd" (ABC, 1991) with Treat Williams as an unconventional defense lawyer. The following year, the actor starred in the Fox comedy series "Flying Blind", playing anxious New Yorker Neil Barash, his characterization often compared (both favorably and unfavorably) to a young Woody Allen. The series, with a supporting cast including Tea Leoni and Clea Lewis, lasted for only one season, but reran on cable's TV Land six years later. No stranger to short-lived series, he starred in yet another in 1994, this time playing a partner in a back-to-nature catalog company on ABC's "Blue Skies". In 1992, Parker had an impressive turn in the acclaimed drama "The Lost Language of Cranes", shown on PBS' "Great Performances". As Elliot Abrams, a young gay man who is growing impatient with his closeted lover, Parker played a character far removed from the awkward and apologetic types for which he is known. More true to form was his turn as writer Eugene Jerome, trying along with his brother Stan (Jonathan Silverman) to break into the big time in the ABC TV-movie "Neil Simon's Broadway Bound", co-starring Anne Bancroft and Jerry Orbach. He also was a credible Eddie Fisher in the miniseries "Liz: The Elizabeth Taylor Story" (NBC, 1995). Parker returned to regular series work in UPN's "The Love Boat: The Next Wave" (1998-99), as seasick ship doctor John Morgan.