What happens if all ladybirds are killed by pesticide?

If that did happen, then any animal that eats ladybugs would also be affected, and since all animals on the food chain are connected by consuming each other, down to the vegetarian animals, which would be affected by the disappearance of other animals, it would eventually affect all animals and eventually even man himself. That's what happens when any animal becomes extinct. Such changes might seem hard to discern now, but the more animals become extinct, the more obvious the changes will become.