EGGLESS CAKE HAS BECOME BRITTLE

Not knowing what recipe you are using, or what sort of cake you made- it's kind of hard to know what to suggest. Egg in cake batter performs a lot of jobs, from leavening to tenderizing, and providing moisture and fat. A cake that disintegrates into powder suggests a failure on a couple levels. It doesn't have anything to bind it together and hold structure, and it obviously lacks moisture. At this point, I think the only possible rescue is to use it to thicken another dessert like pudding.