Couple of reasons for moisture in basements:
Basements are lower in the ground than the rest of your house. The temperatures of the ground is much cooler than air temperature in a house. Air can hold different air levels depending on temperature. What happens when a basement is not properly insulated is that the warm, humid air from the house comes into contact with cool walls/floor from the basement and can condense, causing mold and musty smells. If this is the problem, you need to insulate the basement (insulated subfloor, insulated walls, etc) to prevent the warm air from ever touching anything cool and forming moisture.
External water penetration happens for a variety of reasons . . . clogged french drains, drain spouts not moving water far enough from the foundation, sewer back up, grade around the house sloping the wrong direction, high water table, etc. If this is the problem, you want to look into getting any surface water as far away from the house as possible, and putting one way valves on your drains to prevent backflow. (Sounds like you've already addressed most of these issues with your re-grading.)
There is no reason for a properly finished basement to ever smell musty. Your basement should not be more humid than the rest of your house.
Thank you. I never knew it was not normal to have a slightly humid basement.
After reading many articles about basements, I made a list of every potential problem and started to go through it to determine what is going on.
Then, I fired up the new dehumidifier last night. In 12 hours, it had pulled around 10 gallons out of the air.
After listing out every problem, I returned to a problem I had thought was temporarily resolved. It turns out we have a slight moisture problem due to leaking from the upstairs bathtub. I had known about that, but the problem resolved with caulking. I didn't really forget it, but I got busy getting quotes for a bathroom re-do upstairs that will fix the problem permanently. (Then, the spouse crunched the car and I got focused on that expense...) Well, the problem is happening again. And I found mold!
So, now we're on a mission to get the upstairs bathtub replaced, etc. We actually want to gut the bathroom. Since our house is old, I am slightly terrified as to what we'll find.
Also, I have not yet had the time to save up to for what looks like will be an expensive repair. So, this should be interesting! I will have to move money around and we'll have to be tighter than normal with our funds.
Oh, one other thing. I was able to remove one wall panel. It is a "secret door" to the water shut-off valve. This is a panel I can remove and put back easily. Since I don't want to remove a more permanent panel right before guests arrive, I used this secret door panel to see what I could see. I spotted R13 insulation, which sounded good to me. If they used that on all of the walls, wouldn't that be enough?
Maybe this bathroom water problem is the real culprit?
To check for condensation, I read I could hang a mirror on the wall and come back to check it for droplets. I will do that too.
This post is all over the place. If you read this far, many thanks to you.