Do you also have a moisture problem in your walls? That could cause major problems! I don't know if you can do anything with the tile in place. If you remove the tile, you can apply a waterproofing such as Thompson Waterseal. There are many other similar products, although I haven't used them. They are suposed to seal out moisture in concrete & masonry. They can't be applied over painted surfaces, so you may have to strip your floors. You might be able to apply it over your tile, but it would probably discolor it. You might be able to clean the tile with muratic acid or something similar. Then you can seal the floor. To see if the moisture is coming up through the floor, tape a piece of plastic sheeting to the floor. After a day or 2 pull it up and check if there is moisture on the underside. I would do this test again after you seal the floor, to make sure it is completely sealed. Good luck!