Poor gutter design has damned us again!

1. I woke up this morning and thought, "Wow it really looks like we got some rain last night." Then I went downstairs and noticed Cary had left his running sneakers in the middle of the entryway floor.
2. Then I went to put them back on the boot tray when I noticed it was wet.
3. It was wet because the patch of ceiling above it was dripping.
   
4. GRRR. I had just called the gutter guy to set up a cleaning yesterday.
5. The rain finally stopped. And then the dripping stopped. We have a patch of discoloration about 2"x15" on the ceiling, but otherwise nothing worse happened...yet.
6. My dad came over and diagnosed the problem, and we have an idea what to do next. He also thinks it wasn't related to clogged gutters, so I don't have to feel like a total idiot.
   

PS. We were damned again because a few years ago melting snow leaked in about two feet from where this leak happened, and that time we got a new roof. This time it should be a much cheaper fix.