You're right, once you get "Es no posible" you're pretty much screwed regardless of what the issue is or what you have to say. I remember somebody elses number/line getting switched to mine, and being able to demonstate this to Telefonica and just being told it wasn't possible... I had to move apartment in order to get a working line.

My friend did manage to get Telefonica to run a line halfway up the mountain just to his house after his (Spanish) wife spent some time threatening Telefonica with what I think must have been a blood feud... nobody is quite sure what she threatented them with, but it worked.