Are you burning Wii games or Gamecube games? I'd suggest you try to burn a Gamecube game just to see if that's recognized since the Wiikey disk config I think is written to boot using GCOS.
I'm partially wondering though about the modchip install and possibly your firmware. Can you double check the soldering of the chip?
BTW, I only have Wiikey 1 so I'm not particularly knowledgeable about the new one but I've read that kind of problem with the first Wiikey as well. Good luck!