It's nearly impossible for us to diagnose this without being there in person, but typically wet basements are caused by ground water--rather than a leaky window or the like.
The ground water needs to go somewhere. If the soil can't drain, it builds up pressure and looks for a way into your basement--either via the walls or, more often, where the wall connects to the footer at the floor.
Cheaper/easier things to try first:
- Add/fix gutters and downspouts
- run downspouts further away from house
- properly slope the ground away from the foundation around the house.
- install surface drains (such as a dry river bed)
- have gutters/surface drains go to dry wells
More expensive/complex solutions:
- Install internal footer french drains and a sump pump
- dig down exterior to install exterior footer french drains and waterproof exterior
Fixing gutters and such is fairly inexpensive and a weekend project. Sloping the yard and surface drains are a bit more work, but still in the realm of DIY.
Installing footer drains and waterproofing the exterior below grade, however, is not a DIY project and will cost quite a bit.