What can you do if a turtle egg has broke and the turtle is still alive?

Moisten vermiculite with water (50/50 by weight, not volume--it should just stick together when you squeeze it, but no water should come out). Place this in a plastic bin with a lid.

Bury the egg halfway in the vermiculite, and keep it at a constant 80F. Put on the lid. Eggs don't need much oxygen, so checking it once a day is enough. The turtle CAN survive this, if the egg is not too badly damaged. Keep until it either hatches, or it's so molded and rotted there's nothing left. (Even a little mold won't kill an egg!)