that "moisture" could be coming from anywhere. If it's dripping from the concrete, my first thought is that any runoff or rain might work it's way through the concrete to the cavity space below. You say there are water pipes in there too. hot/cold pipes sweat which could also be a source.

You could store your stuff there and cover the stuff to keep it dry while letting the water take its normal course and go back into the soil.

The concrete pad may have cracks or expansion joints that are leaking, it sounds like an unusual construction in that someone went to all that trouble to build those piers. I am assuming the pad is open to the weather?

Being late winter assuming you have snow, there will be a lot of freeze/thaw going on....the existence of the piers may be actually because of ground water, the underground parking in my old office building had its lowermost level on concrete piers and a plethora of sump pumps, because of ground water.

The other factor to consider is that concrete is not really waterproof unless it is treated, or prestressed. The Romans knew how to make concrete waterproof but we haven't quite figured out how they did it..that's what my Engineer Dad used to tell me, anyway.

Another possibility is that now you've enlarged that hole in the blockwork (I assume you checked whether it was safe to do structurally) - I assume the blockwork is in part of the heated part of the house? - you have effectively added that space to the conditioned part of the house. It could be that humidified air is entering the space and hitting the cold underside of the concrete slab, and creating condensation.

It is not really desirable to have that moisture there, presumably it could run against the blockwork and cause dampness within the house. You are probably violating some codes attempting to use that space as you describe, too. You may need to get an engineer to look at that and determine where the moisture comes from and how to stop it. You may need to add a sump or something, you might have to apply insulation (spray foam perhaps) to the underside of the concrete. Ventilation is also something you may need, I doubt it's advisable for it to ventilate into the house. You may need some sort of "snorkel" type pipe to go up the side to the outside air, it would also equalise the temperature underneath so there won't be the condensation if that's what it is. Get an Engineer in there.... NOT a 'moisture control/basement flooding 'expert' although you may need them later.

Meantime, 1) work out if the moisture is condensation dripping down 2) consider removing the plastic if it is making it worse, although I guess it's keeping the water out of the soil.

Sorry I missed that you had already concluded the moisture was dripping from the underside of the slab...so it's most likely condensation, or moisture ingress from above, or both.

One way or another that needs to be ventilated, as I said ventilating it with the house air is probably not going to be a good idea.

You could also remove what water you can and put a dehumidifier under there, and ideally cover up the hole into the basement or restrict the airflow in the meantime til you work out what to do. The one downside I can see to insulating the underside of the slab with spray foam is it might trap moisture underneath a bit, although the slab should breathe upwards.

You may find the slab stays a bit more free from snow, downside, you are heating it with the household heat. You may also get more ice up there because of this heating.

Eventually the humidity should drop in there somewhat but I still think you need to talk to an engineer about what to do with the space. If you remove the excess moisture then cover up most of the access from the basement, the temps ought to equalise a bit more with the outside which would lessen the issues you're getting now. If you want it to be a 'conditioned' ie warm space, you'll need to line and insulate the space, including the ground. I guess that is an option too, and would lessen your heating load. I suppose some form of supplemental heat in there (a dehumidifier will heat slightly too) could help, for storage, like a garage, you mostly want to keep it just above freezing. Might make a good root cellar or better still, wine cellar. Once things are sorted out, the temp will probably be quite stable year-round.

the moisture is dripping from the concrete 'ceiling'. the new entrance has been blocked off (and has been since this was don). We are in Atlanta and rarely have snow ( or rain at the moment!!) I am not sure what to think. I am reluctant to put in any vents because in the summer the humidity here is very high.
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if you can, you should post some pictures. I don't believe that a driveway slab on piers with an accessible crawl space below is very common and some photos of the dripping would be useful to see what you're talking about.

High humidity would be a very good reason to add vents, you just need to add something that will not allow the ingress of rain etc, like a ship's ventilator....there will no doubt be a proper way to do it, but basically a 4"pvc pipe through the slab suitably waterproofed at the join, two elbows so it points downwards, and bug/vermin screening over it.

It is precisely this humidity that necessitates ventilation. You cannot have an air-filled void like this closed off, even if it was considered 'watertight' it should not be done. Even in a mild climate the slab will cool enough to form condensation underneath, because it will be warmer underneath.

I lived in Australia and NZ for around thirty years and most houses there are constructed without basements but slightly elevated. The bases were either brick piers or brick courses with vents throughout. Dampness and mould in spots like that if they were inadequately ventilated was a frequent issue.

I certainly agree your setup is uncommon. For the reasons outlined above you need a professional to look at this before you do get a serious mould problem. What does it smell like in there?

As I also mentioned, if you've had rain etc, leaks or just dampness of the slab will be enough to cause this - you may also have water entering the space from the surrounding soil.

Some sort of mechanical ventilation may also be necessary or advisable.