You hear about the civilization that rose and fell from power in the eastern hemisphere slot. But was there any kind of civilization that had an amount of influence near what the holy Roman empire had in the Western hemisphere at anytime before Christopher Columbus came?

Before I jump in here, I think you may have your hemispheres mixed up. The Holy Roman Empire is in the Eastern Hemisphere (like the vast majority of Afro-Eurasia), while Columbus is famous for reaching the Americas, which are in the Western Hemisphere.

So are you asking if the Americas had any nations comparable to the Holy Roman Empire in Europe?