It sounds like you have trapped the cool air behind your new drywall and you are getting condensation. There should be no vapor barrier in a basement, because the moisture in the walls must be able to dry to the inside. Any fiberglass insulation in there will absorb water, which is not the direction you want to go.
There is a good article for you to study here- http://www.buildingscience.com/docum...lation-systems
I don't think there will be a lot of posts today because of the holiday, but there are a couple of experts here on the forum who will be likely to chime in eventually.