Matt for what its worth, and I pretty much agree with tmv and Terminator that the ccfl inverter is probably going on one or both lights. Not sure how you wired everything up, but you can leave the "dead ballasts" inside the headlight, and see if you can fish the connections out of the middle of the headlight, and mount a new set of CCFL inverters externally, as its not going to be fun to be opening the headlights for replacement again.
If I recall correctly on your lights, the two ring connections had white wires and were run somewhere in the area of the self level motors, so with a small pick or flat head you can probably fish those out, there should be a small grommet in the middle of the headlight which isn't being used. The other input to the CCFL is the power input which came out of that weird looking plug above the high beam.
The way it works is this, both ring connections plug in one side of the inverter and then the power connection comes out of one input on the other side.
Shouldn't be too tough and the CCFL inverters are cheap to replace:
CCFL Inverters for BMW Mazda Lexus Infiniti CCFL Halo Angel Eyes Kit 1 Pair | eBay