First step in PC debugging in to try and eliminate the causes of error.
You say it wont POST. So take it inside, hook it up to a regular desktop PSU and regular CRT monitor and see if that helps. Since it worked before, I would guess the RAM/CPU/Mobo are compatible so I will skip over that.
Just because the screen works on the laptop doesnt mean it is fine. A resolution could be blown on the monitor and the carPC is trying to use that. If you dont own a CRT monitor, check craigslist for a free one. Nobody likes them, but they are the BEST monitors for debugging purposes. You can send them any signal in the world, and they will try to display it instead of giving up and going blank.