Baby Finches Dying?

Our finches have had their second batch of eggs. Fin the first batch of 5 all of them died. I could see them moving, but they died before they were out of the shell. The second batch is hatching and the first bird lived two days. I found it dead and felt it was important to remove the dead one. Did I do wrong? Do they remove their own? I'm afraid they were caring for a dead one for a whole day and did not feel that was healthy.