That ribbon cable connects the whole right side of the console (AXBY/C-Stick/Power Button), so I'm surprised it even turns on to check if everything is connected properly. Anyways, the only thing that white lock does is press the contacts down so they touch the ribbon cable and lock it into place so it doesn't slip (it's the reverse of the black locks which press the cable down into the contacts).
You have 2 alternatives:
1) Try putting that lock back: I've done this, but it's insanely difficult, since it requires you to pass all the little pins of the connector through the white plastic at the same time you slide the tabs at the sides of the plastic into the board socket. You'll require a magnifying glass and surgeon-like precission to put everything back into place.
2) Get some thin plastic to put on top of the contacts to press them into the ribbon cable so they do enough pressure to make sufficient contact. I haven't done this with the white sockets, only the black ones which are easier to do a workaround for.
