Complex sentence: He served in the Louisiana House of Representatives from 1924--1936, serving as floor leader from 1928--1932 and Speaker from 1932--1936, when he was elected to the U.S. Senate.
Split into simpler sentences: He served in the Louisiana House of Representatives from 1924 to 1936. Ellender was the House Speaker from 1932 to 1936, when he was elected to the U.S. Senate.