Water is coming up at the cold joint that is past the tack strips. I have been told that by installing an interior drain and sump pump that it can cause significant erosion by constantly pulling water from below the slab and footing. I have seen basements that have significant settlement due those types drains and sump pumps. My first recommendation to my client is to apply a concrete sealer to the floor around the perimeter cold joint. They make some high quality specialty sealers that claim to work great. I told my clients that this would be the most affordable and simplest solution, but it may not hold up or be the ultimate cure to there problem. I think that the proper repair would be to install a exterior perimeter drain at the footing, but this would be very difficult to do on this home.