...Chris, is to get that carpet up, yes. If you wish to save it, the carpet could be laid out to dry in a garage. After the carpet, get rid of the real mold problem; the padding, if there is any. Pad will hold water for a long time, and drying it in place is not advisable; it will slow they drying process of the floor and any framing/drywall in the area.
As to waterproofing, do you have a sump pump? Is water in the basement a regular problem, or new?