Ahhh good old system trouleshooting ...
1st, click the Monitor Object and drag the box in the bottom right corner to make it longer so you can see more events in the list.
Press a key on the keystation ... do 5 seperate play events occur? if so, the problem is almost certanly with the signal coming into Logic from the controller.
Next, I'd personally create a new monitor and then drag a seperat cable from the output trangle of Port 1 (ie, NOT the SUM output) to the new monitor and press a key again, see if anything different happens. if nothing happens, then you know port 1 is not the keystation, so you'll need to cycle down through the ports until you figure out which one is the keystation. If there is still 5 events, it's looking more and more like the keystation itself.
You could try throwing a Voice Limiter object in the path and see if that helps ... if it does, you will need to customize your environment appropriatly ... that will take some fiddling around, but you'll probably need to assign the voice limiter before the instrument object you are going to play, and then target the voice limiter in the arrange window.
Sounds easy and fun, huh? The first step though is figuring out where the duplicate notes are coming from ..