Sump pump runs ever 5 min and mostirue in the walls 3 years old house?

I hope you can help me I bought a 3 years old house it about 4000 sqr ft the basement is not finished it a big basement to the sump pump works every 5 min and it has not rained for 30 days. When we purchase the property we did not pay attention but the walls and the floor has been painted. Now all paint start peeling in the first block from the floor about half foot up around most of the besetment wall. We did had little higher level of radian gas so we installed the system, when guys came in to install cut the circle in the floor there was water there. The sump pump runs to a city sever we did disconnected that and running the pipe on the top of my yard about 20 feet away from the house but the sump pump water still running the same. I can't figure out what is the problem moister walls water under a slab and pump working every 5 -10 min do we have a major problem ?? or can we control that. also we did checked all down spots they fine and perforated pipe looks fine to be lowered the camera down but the front of the house have water in the pipe and back of the house pipe is almost dry.