Crawl Space Ventallation?

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My house is built with a traditional crawl space and vents. The idea being that the air will be pulled in and out through the foundation vents. I see now that they have discovered that this does not work like they thought and the better way is to line the entire floor and walls with plastic, along with insulation board on the inside exterior walls. With this method there are no foundation vents.
So my question is..... I have moisture problems under my house. The floor insulation is starting to look like stalagmites hanging in a cave and mold is starting to show up on the joist and air handler. So I have decided to close up the vents hoping to reduce the amount of cold air and humidity coming in the crawl space. If I do this alone and not totally seal off the dirt floor with plastic will I create more problems than I have? Does this new method only work if the entire crawl space is sealed off or can I just close off the vents and see a difference in moisture?