Looking to get form Barranquilla Colombia to Cuzco Peru... any suggestions?

So I'm going to study in Cuzco Peru over winter break and I'm only finding plains to Peru for a couple grand. I found a plane ticket to Barranquilla, Colombia for 79.80 including taxes and I can't imagine that a bus or train would cost more then a grand to go form Barranquilla, Colombia to Cuzco Peru. Does anyone on here know anything about traveling in South America.I would love to see the country side between the two, so I think taking a train would be awesome! Anything? Thanks guys.