hi salaki,
Do you have access to a test voltmeter or an oscilloscope?
If yes, remove the LED, connect the scope in place of the LED, else connect the meter in place of the LED.
Get a strong permanent bar magnet and move if back and forth over each coil in turn.
Keep the magnet 'end' close as possible to the coil and move the magnet quickly.
The scope should show a voltage signal 'jump' , set the scope amp to say, 0.2v/cm, else the meter to 0.1V.
If you get a 'jump' on the scope/meter when you sweep the magnet over a coil the it means that you have continuity in the coils.
I suspect that you have the layout 'sense' of the coils/base magnet disks wrong, so that the generated voltage in each coil is cancelling the other out.
Do the test I suggested and lets know what you find.
EDIT: you could also use the bar magnet to check the orientation of your magnetic discs, 'repulsion or attraction'.
EDIT: I have to ask, is the LED wired the correct way round and in good condition.?
Try spinning the turbine in the other direction, in order to check the LED wiring sense.