Final answer:
The country that played a significant role in World War I but did not join the League of Nations is the United States. The U.S. Senate's concerns about joining the League fueled a movement toward isolationism and contributed to the League's ineffectiveness in preventing future conflicts.
Step-by-step explanation:
The nation that played a major part in World War I but never joined the League of Nations is the United States. Despite President Woodrow Wilson's vision for the postwar world, which included the creation of the League to promote global security and prevent future wars, the U.S. never formally approved the Treaty of Versailles nor joined the League. The U.S. Senate, dominated by the Republican Party, had significant concerns about the implications of joining the League, particularly the fear that U.S. troops could be sent into international disputes without Congressional approval, undermining the Senate's constitutional power to declare war.
The United States' decision to remain out of the League contributed to a shift toward isolationism after World War I. The League of Nations' ability to mediate and resolve international disputes was thus weakened without the participation of one of the world's most powerful countries. Ultimately, the League's ineffectiveness in preventing conflicts later became one of the contributing factors to the outbreak of the Second World War.