Happened to be home today during a nice rain. I spotted a few "problems" that I think could explain where a lot of the water that gets into the basement is coming from.
The rear guttering is hopelessly overwhelmed. The water can't run down the single downspout fast enough when perfectly clear; now imagine if a few leaves and stuff were in the way too....

All this water hitting the ground--- it's hard to see in this picture but there's 3 inches of water pooling here and flooding the patio area.....

Now I go around front. Check out the Downspouts into French drains. First one is backing up big time....

And the Downspout on the side of the Garage---- It's full of water.... if you can see in this image water is shooting out of a nail hole under pressure.....

A lower angle showing more water from the spout. This pipe is either completely filled or blocked but it's sure not draining anything!

And last but not least.... It took me awhile to find out how so much water was getting in the garage. It was a mystery--- under the door? A leak? Couldn't find the source !! Well, here it is: The condensate pipe for the A/C-Furnace! You see apparently the previous homeowners thought it would be a good idea to connect the condensate line to the french drains the downspouts use. So when they backup, water backs up into the garage. This is actually after most the rain had stopped. It had been shooting out with a lot more force....

Looks like I have some work ahead of me. I need to revamp the guttering and draining of this place. If I'm lucky though I'll nip a lot of the basement water issues in the bud.....