The ants you see are probably carpenter ants. Carpenter ants create tunnels for nesting purposes in moist wood. They don't kill trees, but they do take advantage of a tree that already has internal decay. Insecticide granules will kill ants that are there now, but others will eventually return. Read more about carpenter ants at:
Carpenter Ants

From your description it sounds as if your tree suffered severe damage when the one limb broke off. Perhaps it was already weakened by internal decay? There is not much you can do to remedy the situation. Read more about storm damage to trees and treatment at:
Storm Damage

Even with internal decay, a tree can live a long time. However, depending on where the tree is located and how large it is, it could be a hazard to people or property if it were to lose more limbs or blow over. Read about hazard trees at:
Hazard Trees

If you really value the tree, you might consider having a professional certified arborist take a look at it and advise you on your best course of action. Read about how to find an arborist in your area on their Web site:
Certified Arborists