Unfortunately, you will most likely need to do some more investigating. Moisture in a basement is one of those problems that can run the gamut from "Meh...nothing to worry about..." to " Honey, we need to sell both children to pay for the repairs."
The lack of vapor barrier could be a concern but not automatically the culprit. I'm assuming the basement was permitted?
This is what I would do in your situation:
1) Check that your lot is graded away from the foundation and your gutters and downspouts are clean, functional and ALSO extend away from the foundation. This is the easiest to remedy.
2) Do you have a a sump pump? Check the pit and see if it has water in, make sure the pump is functional and the drainage pipe isn't blocked.
3) Check around (building department, local builders) and see if your area is known for having a high water table or if others in your neighborhood have had basement issues. If yes, sometimes a sump pump / drain tile can help, although retrofitting these can be fun.
4) There are a number of really good basement water proofing systems available. However the do involved excavating down to the footers. This gets really expensive to pay a contractor to do it. If you're handy, you can do this yourself, but it's a lot of dirty, nasty, hard work and you'll need to be familiar with exactly how the system should be installed otherwise all the work could be for nothing.
I would let the dehumidifier do it's thing and check gutters/downspouts/grading first. Changes are very good these will help the issue. If not, pay a PE to come in a do an assessment and give you your options.
My .02
