I took it apart and stopped before step 6. Took it to an experienced radio repairs man. I think he did a good work soldering three point for £5 but I forgot to check the headphone jack before taking it back home and 'of course' the jack is not working any more. I've did everything I could find on internet to make the jack work again but no.
I doubt it could have broken in the repair but who knows...
Anyway I've ordered a spare jack from Amazon for £5 and I'm thinking of changing it myself.
Unfortunately though the ipod has given up totally on me now. I can't even make it wake/start up connected to iTunes. Oh, dear! my good old friend, won't you please come back to me?!