I have water in my heat vents. My house is on a slab. Any suggestions?

If it's rainy, or snow is melting, my heating vents in the floor fill with water. My house is on a slab, so there's no basement or crawl space. I'm not even sure who to call about this. After a couple of days of the water being there, it gets "mildewy" inside, and extremely humid. Any suggestions are appreciated. Thanks!