The Inca were actually a tribe in the Cuzco area. They had their own kingdom of Cuzco under the leadership of Manco Capac in around 1200. This Empire was split by a war and consequently was conquered in 1533 by Francisco Pizarro.
There is no sign of any surviving Inca. Those who were left from wars and conquerors actually were lost to other nations. They got married into other nations and lost their identity forever.