The Inca ruler captured by Pizarro and held in the Ransom Room was Atahualpa.
Pizarro captured Atahualpa during the Battle of Cajamarca on November 16, 1532. The Spanish held him in Cajamarca, in the building traditionally identified as El Cuarto del Rescate, or the Ransom Room. The surviving structure is now a historic site in Peru.
Atahualpa offered to fill the room where he was confined with gold as high as he could reach, and to fill two additional rooms with silver. Treasures were collected from across the empire and melted into bars, but the ransom did not secure his release.
The Spanish instead tried Atahualpa on charges including rebellion, idolatry, and responsibility for Huáscar’s death. He was executed in 1533. Huáscar is an easy confusion because he was Atahualpa’s rival in the Inca civil war, but he was not the ruler imprisoned in the Ransom Room.