Baby Black-Capped Chickadee, What do I do?

My mother and I have been having serious problems with our neighbors cat lately and we had came across a nest the cat was getting into. We do not know how many baby birds had started out but when my mother retrieved them, there were four baby black-capped chickadees in the nest. My mother brought them inside, fed them some of her ground up kitten food which he uses to help her baby finches. She put them in her aviary with her finches. A few days later I noticed one of the baby birds was face first at the bottom of the cage. Mother said the baby bird was dehydrated and I had to quickly feed her water gently through a syringe. But it was too late and the baby bird died in my hands. Mother was at work when this happened so I took the rest of the baby birds that she had put in the aviary (Even though they didn't seem to have any signs of being sick) And fed them water through a syringe. I put the baby birds in a separate cage from my moms finches and watched them all carefully. The next day 2 more baby birds had died through that night. Mother told me about the colors of their waste and how they poop and pee at the same time. She told me that they are only peeing. There is no poop so that means they were dying from not eating and that they had been starving for awhile. She said that the mom and dad birds had left them. Now mom and I are panicing. 3 of the 4 baby birds has died and we can't get the remaining bird to eat. My mother is very good with birds and she had to resort to force-feeding him. She said its very dangerous but if we hadn't he would have died. So my question is, how can I help this last baby bird so he can survive? I'm at my wits end here and am scared he wont make it. He is old enough he is flying now but not enough to eat by himself. Will he start eating by himself soon? or do I have to show him how? What can I do to help?