tYou can't use cigarette lighter.
If you have you laptop, LCD and PS2 running at the same time it will be to mutch AMP needed and you are risking to burn cigarette lighter cables. (to mutch power)
It could work, but If it was me I will not risking damage of ciratett lighter instalation.
I will post you a schame of my procject leater then you can see how I am done it.
PS sorry, my write-english is not to good.