My wife and I purchased our first home a couple of months ago. It is a 1950s Cape Cod located in the hills of western MA. The main issue we are dealing with is the damp basement. This is due mainly to two issues. First, the previous owners had the gutter water dump right at the foundation. To fix that I am installing an underground drainage system to take all that water to the storm drain.

Second is the condition of the basement concrete floor. There are a number of cracks, and the previous owners seemed to have dug up small portions of the concrete floor. This leads to capillary dampness around the cracks.

My question then is whether I can fix the capillary dampness by repairing the cracks with new cement (perhaps special cement is waterproof?), or whether the only way to really fix this is to pour a new floor entirely? TIA.