Our gymnasium was built over 35 yrs ago. They did not put any moisture barrier under the concrete slab floor. Moisture constantly comes through and times with a lot of rain, water even comes from where the walls meet the floor. We run a humidifier to keep the moisture and mold down. We have a very small budget. The building is a pole barn type. The gutters are good. The floor is bare concrete. When it was first built we literally had dirt and mud come in where the wall meets the floor. They put more cement blocks (higher) on the outside of the foundation. This stopped dirt from coming in but not moisture. What can we do on low finances.
It sounds like you have two problems.
Water is coming in through the space where the wall meets the floor.
This can be mitigated by making sure the surrounding terrain is sloped away from the walls, ensuring that surface water flows away from the structure. You might also be able to dig out the foundation and seal the soil/structure boundary with a heavy plastic such as Delta Board.
The other problem is likely what's called rising damp. This is water underneath the foundation that wicks up through the concrete. The solution is expensive. You need to excavate the foundation, Install weeping tile which drains to a safe location. This will help keep ground water out from underneath the foundation.
Since you say this is a barn, the foundation may not be that deep, and it's something you could do yourself. Just be sure to fully research (or ask questions here) how to do it.