Some serendipitous connections got him onto the New York stage as an actor, followed by his venture west to Hollywood, where he began acting in little theatre and landed his first film role, in the 1934 picture starring Spencer Tracy, Looking for Trouble.

[4] Returning to New York, Conway acted on Broadway in plays that included Angel Island (1937), In the Bag (1937), Mimie Scheller (1936), Summer Wives (1936), and If a Body (1935).

[6] By the mid-1940s he was a contract player for RKO Radio Pictures, and he was chosen to portray Chester Gould's comic-strip detective Dick Tracy in a new series of feature films.

RKO's earliest publicity photos posed Conway in profile, hoping to emulate Gould's square-jawed caricatures.

In March 1948, Conway announced plans to launch an independent production company, intending to make one film per year;[9] he already had two scripts in mind, titled "Condemned" and "The Twins."

According to one report, "Morgan Conway was upset when itemed as being in the company of a star whose after-dark drinking bouts disgrace the whole town regularly.

Morgan Conway was considered for the leading role in a film biography of New York mayor Jimmy Walker, to be produced by Gene Fowler,[11] but the project was abandoned.

"[12] In 1948 Conway became a goodwill ambassador to Mexico, presenting a patriotic American film, Of This We Are Proud, to the Mexican consul for showing to schoolchildren.