Recently, I was using one of the sinks in my laundry room and I felt a drop of water hit my face. At first I thought the water had splashed up from the sink, but after a couple more drops, I looked up and noticed water droplets on the ceiling.
I went up to the attic to find where the water was entering the house from the outside. I found a pipe from an old exhaust system, and it was wet. I went onto the roof and found the end of the pipe. I couldn't tell for certain that there was a gap between the pipe and the roof, but I assumed that was the issue.
So, I bought a can of sealant from a local home improvement store and sprayed the product liberally around the pipe and the surrounding roof tiles. That was some time ago, and we have had a few rain storms, and I haven't seen any more water droplets on the ceiling.
I don't know whether this product will work for your basement leak repair, but if you visit your local home improvement store, one of the workers can point you in the right direction.