Ok, I've looked all over the internet, tinkered with the ideas I came across and these are my conclusions:
The shift key won't light up unless you're connected to your Mac. Eventhough I could eventually power the keyboard, the LED (indicating that the KB is trying to pair) was blinking, the shift LED wouldn't light up.
I disassembled the KB, and trust me, it isn't necessary at all. The problem is the + contact, it seems that the battery contact just isn't abble to conduct current.
I resolved this by rolling some soft household metal sponge, as recommended in a previous post, into a small ball and dropping it directly on the contact, then jamming in the batteries. Don't worry, the case will close (my ball was about 75mm in diameter). I've been told that is nevertheless important that the metal sponge doesn't touch the casing, this could cause a shortcircuit. I'm not sure this is accurate, but it seemed pretty plausible.
My keyboard worked just fine after these steps. Try this first, if it doesn't work, then try opening up the enire thing, it's pretty delicate in there and there's simply no way, without beeing somewhat of an engineer, that you can reach the + contact by removing the hardware as described in te previous post.
I hope this helps some of you out, I wish I had found a post like mine when I first tried googling the issue ;-D
Cheers,
Sander