A mother american robin has abandoned her three babies on my balcony. Can i help them?

A robin built a nest on a lamp on my balcony. we dont use it much, so i thought we wouldnt scare her off and i let her leave it. She laid three eggs, incubated them and they all hatched. If i noticed she was out of the nest i would sneak up there and take a picture. Now i havent seen her in days, the nest is falling apart and the babies are gasping and looking terrible. the local DOW cant help as robins are not protected... "circle of life kinda thing" they said. i feel really bad and so do my kids. is there anything i can do? (even its to help them die humanely we would appreciate advice on that, too. its hard to just watch them suffer slowly. its cold out there at night.)