If it's ground water, the issue isn't water vapor, but rather just plain water. Is the water table close or higher than your basement slab? If so, not a whole lot you can do to completely stop moisture issues, as that basement was just built in a bad spot.
That said, the main solution would be a sump pump and drainage tile system. Any water coming up through the earth dumps into the drainage tile, into the pump well, and gets pumped out. Again, though, if the water table is already higher than the basement slab, that'll be a never ending battle as well.
That said, perhaps the issue isn't as much about ground water as you think. Does it get humid in your region? If so, then 'damp' basements are par for the course. Basement walls are usually always going to be cooler than the air, and, a such, will be were condensation forms in a humid environment.
To prevent that, you need to a) dehumidify and/or b) insulate the walls.
A dehumidifier constantly running tends to be a normal part of any basement in a humid zone, so that's a good start. Insulating with walls with XPS or EPS foam will help too, it'll keep the moist air further away from the cold wall.
I can't say if an air exchanger would help or not. If it's including an A/C system, it could help (as the A/C is a dehumidifier) but otherwise I have a hunch you'd just be pumping more humid air into the space.
Products like drylock don't do a whole lot. They're not strong enough to prevent hydrostatic water pressure (high water table) and do nothing to prevent condensation. They're a bit of a gimmick.
Try installing a vent in the door, it will allow the room to breath. Make sure the exhaust from the dryer is sealed all the way around where it exists the wall, then go outside and do the same thing. Check the roof edge and make sure you aren't having water drain behind the gutter into the wall. Then climb into the attic when it rains with a big light and watch for water.
Also, get rid of that mold.. it's really bad for you.
Best Answer
Take my advice with a grain of salt – I live on an extremely humid island – but my dehumidifier can be set not to work below certain relative humidities, and those are 40%, 60%, and 80%. A quick googling turns up a number of sites that suggest 40%-50% as the ideal range for health and comfort.
It may depend on where you live (Arizona?), but the 16%-22% you're seeing strikes me as very low. If that's what humidity is like throughout your house, even without the dehumidifier, I think it's safe to say you don't need one. I would wager that they don't really make consumer dehumidifiers that can remove moisture too far below that.