Are the walls damp? If so, the first thing to look at is the drainage around the foundation. Do you have 10' of downhill slope away from the foundation walls with a drop of at least 6"? Do you have at least 6" of exposed foundation wall before dirt starts? Do your gutters work and do your downspouts channel the water from the roof away from the house that same 10 feet? A little regrading and getting the water from your downspouts away from the house might solve 90% of your problem.
I have a high groundwater problem. I just had a perimeter drain installed around the house last week. My wet problem is solved forever but I wouldn't wish my excavator bill on anybody.