Water traveling along heating duct work in the third floor of my side split home?

I have a 4 level side split home, the kind with a full basement (4th level) and a partially underground 3rd level that is finished. We have a re-occurring issue with a trickle of water coming into the basement via a heating duct that goes under the floor of the 3rd level and services the rooms on the 3rd level. The duct work comes into the basement via an interior wall, and there is NO OTHER WATER in the basement (it's bone dry). The water comes in when we've had a lot of rain / soil moisture. We removed the duct work, and the water is traveling along the vent from the far end of the house. It looks as if there is no "cap" on the end of the duct, which abuts against the foundation wall. The ductwork has a small layer f sediment in it. Where is the water coming from? The duct is below grade and is likely below the footings of the house. There is not crawl space. I am having two sides of my foundation excavated, re-tiled and water-proofed. It that going to solve the problem? I am frustrated because I pointed out to various people that the water was trickling out via the duct work, and that I felt the water was coming in via a weak point and going down the path of least resistance. Nobody took the duct work of to look before starting this job, and I was told the issue was the result of blockage of the weeping tiles and possibly a crack below the ground. There is no crack, and the tiles, although they have some sediment, are less than 1/4 full. The soil around the house is not even terribly wet (despite all the rain). Mt neighbor has a downspout that goes directly into their drainage below ground (which is not legal anymore) on the side of the house where we seem to have a problem (maybe). Is it possible this is contributing to my woes??? Does anyone have any idea what is going on? I'd rather not rip up the floor of the 3rd level, as it has only recently been finished - and I am going to be selling my house.