@ted - genial idea! Thank you very much!
My 4.7 uF cap got lost. So I use a 10 uF cap.
Mysteriously, the LED lighted! (she happy, me happy :-)). Using both the white ferrite ring and the blue ferrite ring.
With the cap, the white ferrite circuit seems to be less brightly than without the cap.
I didnt measure the current in both cases (with cap and without cap), so maybe is just an illusion.
+++
Ok with the classical and simple Joule thief, magnetic field etc. I can explain that, first to myself.
But I cant figure out what the cap does in this case. My first thought is that it changes the frequency to fit what the transistor can commute. But I maybe wrong.