[billybek]

I think someone suggested this already.
Break a section of slab in your basement and install a sump pump first. See if your problem goes away.
Some locations frown on discharging the sump pump to the sanitary sewer and it must be discharged back outside.
When I put some new footings in the basement, I scored the floor with a diamond blade in the circular saw. I used my shop vac with a high efficiency filter to grab some of the dust and also sprayed the blade with water to cool it down. Once you have made a couple of passes fill the cut groove with water to cool the blade as you cut. I also used the hilti drill to drill along the cut line every so often and broke it out with a sledge hammer. Slab was about 2-3 inches thick.