The adhesive used is probably a black mastic which was trowelled over the entire floor. This was also thought to act as a vapor barrier. Before you rip up the floor, check out your site drainage. Sounds like water is getting under the slab and could be remedied by a simple gravel drain along the perimeter of the house. You can also incorporate perforated PVC pipe if you feel there is that much water. Still lots of work, but it won't disrupt your house to the same degree.