The problem with SCART connections is that there isn't a firm agreed standard of interfacing between the various consumer electronics manufacturers. I've always disliked SCART connections for this reason. But, SCART is everywhere so we can't get around it, can we.
At this point I think you need to start measuring some voltages on your SCART connections. I can advise you of what pins to measure, and what results to expect, but firstly do you have a decent multimeter you can use? And are you amenable to taking some voltage measurements?
Regarding the in-line resistors, I think these are used as a kind of crude voltage divider. I think they may even be specific to the requirements of an LCD TV's SCART input, but I've never used SCART on an LCD so I'm not too sure about that.
The 1K in-line resistor on the switching pin (pin

may be there for current-limiting reasons, so that you're not connecting a 12V output directly to the input of the LCD. Or, if the LCD's switch input pin is designed to trigger on a voltage lower than +12V (as I said, no agreed standards! Arrrgh!) then perhaps it is there to form a crude voltage divider.
Either way, we need to see some voltage on key pins of the cable before we can figure out what's going on.
AH.