For this sort of support or help, you probably need to engage one of the (training or consulting) partners - https://partnerdirectory.atlassian.com
As for the question summary though - columns are collections of status. A move of a card from one column to another is actually a transition from one status to another. Transitions are defined in the workflow, and can be protected.
So I would guess that when you're unable to drag from one column to another, either there is no transition from the status in the source column to any status in the target column, or there is, but it has conditions on it that are blocking the move (user must be in group X, field Y must be filled - that sort of rule)
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