Andy Dufresne was sentenced to two life sentences, how was his right to appeal his sentence denied to him by the warden, and could he have been able to appeal? How?
The right to counsel was decided by the Supreme Court in Gideon vs. Wainwright in 1963.
Gideon v. Wainwright was one of a series of Supreme Court decisions that confirmed the right of defendants in criminal proceedings, upon request, to have counsel appointed both during trial and on appeal.
This story is based in the 1940s or early 50s at best. This is evidenced by the Rita Hayworth poster Andy requests. A screencap of the poster shows an image that comes from Life magazine in 1941. Prior to Gideon, lawyers were only appointed for capital offenses (execution). Since he was convicted of killing the only means of outside support, the wife, and her lover, Andy couldn't afford his own lawyer; he had no recourse. The warden was also corrupt, and the staff of officers supported him. They control Andy, control his contacts, control his whole life, just as a convict.