How Hitler managed to gain control over whole Germany?
Answers
There are a lot of reasons and "people were desperate for change" does not account for half of the legal intricacies of changing a democracy into a dictatorship within 5 months. Here are the highlights:
People did not have a preference for democracy
Democracy had only arrived in Germany in 1918 and it was immediately blamed for losing WWI (the first act of the democratic government was to sign the disastrous Versailles Treaty) as well as the hyperinflation of 1921-1923 and the mass unemployment of the beginning 30s. Given such results in just 15 years of democracy, who would not reminisce about the time of the emperor?
Of all the democrats of the Weimar Republic, the people most liked President von Hindenburg, who was a monarchist and had been the head of the German army under the emperor before becoming president of the Weimar Republic. In a way, President von Hindenburg represented the strong leader principle even before Hitler came to power.
The Weimar democracy was a poor example of democracy
There were so many splinter groups in parliament that nobody could ever agree on anything. Parties would ally in order to depose a government but then were unable to agree on an alternative candidate, leading to 5 general elections between 1930-1933. People were tired of voting. Also, the elections were not free, in the sense that Hitler's SA routinely positioned themselves outside polling places, preventing access or beating up people who might vote for other parties. There had been open street fights between Nazis and Communists since 1931 with at least 130 dead.
Paul von Hindenburg elected Hitler
Since parliament was basically not operating, it was up to the President Paul von Hindenburg to rule the country through "emergency decrees" and by naming the next government. von Hindenburg was opposed to Hitler, whom he despised for his low military rank, but eventually his friends among aristocrats and military convinced von Hindenburg to give Hitler a chance to fail, to hopefully disenchant people.

Hitler and President von Hindenburg in 1933
In order to ensure that Hitler would fail, von Hindenburg put him in a government with Franz von Papen, a centrist. President von Hindenburg had made his confidante Franz von Papen chancellor for a few months in 1932 and he became vice-chancellor in the Hitler government in January 1933, promising the president that he'd "push Hitler so far into the corner that he squeaks". The position of chancellor was mostly that of a chairman at the time, with cabinets using majority voting to make decisions, and other than Hitler, only two other Nazis were in that cabinet (in powerless positions) and he was opposed by 8 conservatives or centrists like von Papen in influential positions in his cabinet. Hence the idea that he could be controlled and made to fail.
Hitler was quick and not so democratic
Instead, the