Insulated Duct Work

We discovered the problem with our condensation on the first floor was due to the concrete floor in the basement . We use a coal stove in the winter and it seemed to "pull" the moisture thru the concree. I was able to temp solve the problem by covering floor with 4ml plastic. It does a great job keeping the humidity to a reasonable level. Now that we want to finish the basement can we have wall to wall carpet installed over the plastic? (There isn't enough height to lay a sub floor.) The plan is plastic, padding carpet.

I have an humidity problem in my basement. In the summer it ranges between 70-100% (RH). I think it's because of an attached crawlspace (about 8x10, 4' high) that has appears to have no floor. I can't close it off because it's where the sewer entrance and the basement is the only access to the crawlspace. Any ideas about how to resolve this? Would something like laying down 3mil plastic in the space prevent the water from entering the air in the basement from the dirt floor? I thought about concrete but I'm not sure it'd be too doable in such a small space, and I don't know how to do a concrete floor from scratch.