Sounds like a possible termite problem...

Especially since you found dead black ants in the area. A termite colony will swarm out with black ants. Once they leave the colony, these swarmers actually do die fairly quickly after leaving if they don't establish a new colony. Sounds like to me you might have a colony and they swarmed. Once you get past this swarm, you may notice the ants have "disappeared". But actually the core colony will stay hidden and continue to eat. If I were you I would get someone out to make sure you don't have a bigger problem...

oh btw, I'm no expert. I just signed a contract to start construction on a new house build here in Kansas City. Then as fate would have it a couple days later I experienced the same problem you described in my current home.