The EE's themselves are kind of interesting. Yes, one of them, the buttons don't work and the trackball light doesn't come on which makes me think there may be a loose connection somewhere. If I can figure out how to get the thing apart, I'm going to see if it's anything I can fix. Even if I can't, it still makes a great battery charging station.
Getting them apart should be fairly easy, just lift all the rubber strips and pads - inside and outside. Remove all the screws and do a little wriggling of the outer cases. You might need to use something like a guitar pick to run round the joins if they don't lift off.
One thing I would ask. If you do take one apart could you please try and take some photos with as high a resolution as possible and post them or PM me and I'll tell you where to send them. I ask this because I don't want to take my working unit apart - it is in almost constant use - even though I did investigate how to do so.