Where should I plug the black cable with the orange end? I can't find its place.

 

That's a GM column and that wiring looks like it is for a cruise control .

 

i think it's related to the automatic transmission. this gives a signal that the transmission is in P position. my problem is that i can't put the key in the lock position and i think it's because this cable isn't plugged in.

 

Looking at the picture again I can see the ignition switch is all the way over to one side , have you tried moving it ? Check to see if the wiring you are talking about goes to the turn signal arm .