I looked and there is no lead that is tucked inside the pipe that I could see with a flashlight. The outside of the pipe looks like all is tucked in and caulked well.
I bought some pvc pipe yesterday (a candy cane type shape) and put it on the top of the pipe to see if maybe preventing the rain from entering the pipe might solve the problem... who knows? The guy at Home Depot thought I was a nut because he insists that water wouldn't leak out unless it was filled up with water. I see his point, however with all the joints that I can see down in the pipe (and all the debris) and knowing that my home was custom built (and in some ways not very well, I might add) who knows... maybe a joint has come loose or something and water is getting out. The amount of water seems minimal... wet drywall is only about 5 " across on the wall and ceiling.
So... right now my house has a "Cindy Who" pipe and I'm just waiting for rain today or tomorrow to see.
If this doesn't work, I guess my only alternative is to call a roofer. Drats.