What part(s) of the Constitution were in question in the McCulloch vs. Maryland case?
Specifically, the issue was the extent to which the federal government could use "implied" powers. The decision, as articulated in John Marshall's opinion, established that not only could the government rely on implied powers to operate its bank free of regulation by the state of Maryland, it could further call on and expand those implied powers in ways that would greatly increase the scope and power of the federal government.
In its most basic sense, the idea that a state could tax or penalize a federal institution within its borders would have taken the nation back to the days of the Articles of Confederation, where the central government had virtually no power to do anything except request from the states things such as tax dollars and volunteers for national defense. However, Marshall's opinion took the principle of national supremacy far beyond the issue of the national bank located within the state, and established a precedent that would later give Franklin D. Roosevelt a firm footing on which to base his New Deal programs.