Was the growth of unemployment after 1929 the main reason why the Nazi party was able to take power in Germany in 1933?
I think that the growth of communism was a far greater asset to the growth of National Socialism than unemployment. A number of communist agitators, such as Rosa Luxembourg were a threat to the Weimar Republic. Most of Hitler's rhetoric was directed at the presumed Communist threat. The fire which destroyed the Reichstag was blamed (correctly) on a communist agitator, and allowed Hitler to insist on implementation of the Constitutional provision for rule by decree.
Although unemployment was a major problem, the National Socialists spoke more against the Communist threat led by international Jewry (since many Communist agitators were Jewish) than anything else. Propaganda was also a major element, as it was used to recall the days of German glory which they promised to restore. They considered the Communists as a threat to this German nationalism, since Communism promoted an international rather than a nationalist theme.
Incidentally, "Nazi" was a pejorative term. The correct term--and the term which they called themselves--was "National Socialist."