We built our home two years ago. Had trouble with the air conditioner, but a new company created zones and now the temps in each room are all withing 3 degrees of each other. However, we are fighting humidity in two of the rooms. Our den has one window and one french door which leads out to our deck. Attic is above it, bathroom, family room/fireplace next to it, guest bedroom below it. Our bedroom has double french doors that lead out to our front porch. The bedroom is over basement storage space with a dehumidifier which runs continuously. Has bathroom, hallway and foyer on the other sides. No leaks have been found. If we turn off the dehumidifier so it doesn't keep me awake, it is humid and smells musty the next morning. Same thing in the den. That dehumidifier must be running all of the time or it smells musty and feel icky. Any suggestions?
to me it sounds like your moisture problem is from the basement. You may not see leaks but to moisture concrete can be permeable. To find out if this is the source of moisture tape a trash bag to the floor for 24 hours. When you pull the bag the next day if you have moisture on the bag or this area of the slab looks wet you have found the source of the moisture. I have had this same issue and found an epoxy floor coating drastically reduced the moisture. We still used a dehumidifier but it was only collecting a small amount of moisture compared to untreated slab. If you go this route you may have to wait until late summer so the ground water is less and the epoxy will bond. Or find one that will seal with moisture in the slab. I have done this on a full basement and a daylight basement and had great results on my own homes.
Air conditioned air is much dryer than outside air, because it is chilled down to about 50 degrees. Cold air can't hold nearly as much moisture as warm air, so this "wrings the moisture out of it". By the time it mixes and rises to 75 degrees again, it is quite dry (for 75 degree air).
The sun is a huge fusion reactor. Every square metre of sunbeam has about 1000 watts of heat in it. (100W per square foot). Some of it reflects, but this varies by the reflectivity (albedo) of the surface - pure white paint reflects 91%, most colors are quite poor, and a lot of roofs are practically black. Think about how big your house is from the sun's angle/perspective, subtract out reflectivity (which on a common roof will be nearly zero), and you see your house is absorbing many thousands of watts of energy. Multiply by 3 for BTUs/hr. This is far and away the heaviest load on your A/C. Humans, computers and even cooking pales by comparison.
Here's the important part: solar gain is not equal. It punishes top floor, south and west facing rooms much more han others.
So, previously, your A/C distributed cooling evenly throughout the house. This meant the dehumidification inherent in A/C was evenly distributed, however, the rooms suffering from solar gain were much hotter. You had the A/C balanced, to put much more cooling on the rooms with solar gain, so the temperature equalized. Since the north/east/low rooms get no solar gain, they also get little A/C - and thus, little dehumidification.
Against that, you have a rather wet basement. Concrete is porous. Water can move through it. Typically water which permeates through concrete immediately evaporates, so you don't see wet concrete - but if you lay a plastic sheet down on it, or set a cardboard box on it, that evaporation will stop and it will be seen under the plastic or damaging the box bottom.
Concrete has no tensile strength, so putting a coating on the inside of concrete is a lost cause. Th concrete the paint is sticking to will just crumble, and the coating will be pushed off by water pressure. The only place a barrier coat will work on a basement is on the outside, i.e. The plastic barrier you laid down before you poured the concrete, or a coating put on the walls before they are buried. Nobody was thinking about that in the old days, so it wasn't done and it's impracticable to do now.
The best way I know to dry out a basement is to use French or Buckeye drains to remove the water from the soil outside the basement - i.e. Lower the water table locally around the basement. It really helps to have land on a slope so you have somewhere for the water to go.