Vertical cement wall in the basement (close to the foundation slab) is leaking around where the drain pipes were replaced by somebody long time ago. They poured bad concrete around input / output pipes (drain, etc). Concrete has cracks, and it is leaking. I plan on exposing the cracked concrete by digging the soil outside of the house and then sealing the bad concrete from outside.
I would fill in the gaps with a good quality silicone caulk formulated for use on concrete, then coat the entire area with a product like Tuff Coat 2 an acrylic foundation water proofing coating. You can purchase both products at your local Home Depot.