Wet smell, finished basement, aggravates when it rains -how do I find the source?
Having vapor barriers in most basement environments is a really bad idea.  Really these only are a good idea in extremely cold environments or when a basement is truly a "basement" - meaning it is completely below ground level. 

It is highly likely that water is saturating your foundation and then not drying quickly because of the vapor barrier.  But there are just a ton of reasons:


Given you have carpet the moisture could be seeping in from the floor and staying in the carpet a bit.  You may not even notice this but the carpet becoming constantly a little damp will make it smell.
It could be just water trapped in the walls because of the vapor barrier or trapped in the insulation itself.  This will not be totally fixed unless you tear down all the drywall - or enough to take vapor barrier and bottom insulation out.  See people 10 years ago and even now thought that insulating your basement walls top to bottom with batts fiberglass was the best way to do it.  Well it traps water and causes mold growth and provides no cost savings in most regions.
You could have a leak.  Basically you will probably need to untack carpet or flooring around the perimeter to see if water is leaking in.  I doubt that you have a real leak and not see any moisture at all underneath your walls.  


Dehumidifiers are for very small constant humidity problems.  When you have a "smell" problem the dehumidifiers are hardly ever going to fix the issue.  You either need to seal your basement better from the inside or outside, remove the vapor barrier (that is probably just amplifying a bigger issue), and the easiest and most helpful thing is to increase airflow.  If you have windows trying to keep them open a lot.  If you have stairs that are near an outside door trying to get the airflow circulating.  I have even seen people run fan to their attic to recycle air in basements.