In the end bought a new card and it wasn't useful of course.
The connector on the motherboard had a pin being pushed out by the plug.
So tiny it took me a very long to notice it.
I was lucky enough to be able to simply push it back in and get the whole thing to work again.
In the meantime, while removing the display to access the WiFi card I got a problem with the graphic connector :) That was bad: the golden very thin part that goes over and around the connector went out for some reason.
I was able to put it back with a bit of reasoning and a lots of luck I guess...
Never had so much trouble with a MBP before. I guess the fact that it was a first generation full alu body machine didn't help. Obviously connectors weren't very good at the beginning.
The lesson is: just be extra careful with connectors, even if they look pretty solid in general...