I was cleaning my gutters twice a year in Parma until my neighbor asked why I never checked the downspouts
For 6 years I climbed up on the roof every spring and fall to scoop leaves out of the gutters, but last October my neighbor Sal asked if I ever flushed the downspouts and I had no idea what he meant. Turns out two of my four downspouts were packed solid with shingle grit and leaves going back who knows how long, which is why my basement got damp after every big storm on West 54th. Has anyone else found their real water problem was hiding in the downspouts instead of the gutters?
The part about "shingle grit and leaves going back who knows how long" is exactly what got me too. I had the same deal, gutters looked fine from the ground but the downspouts were basically clogged pipes full of mud. Water has nowhere to go so it backs up and finds the weak spot in your foundation, which in your case was the basement wall. Check the bottoms where they drain too, mine were dumping right next to the house and making it worse.